#Loading Libraries

library(GGally)
## Loading required package: ggplot2
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library(boot)
library(ggplot2)
library(tidyverse)
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## ✔ tidyr   1.2.1      ✔ stringr 1.5.0 
## ✔ readr   2.1.3      ✔ forcats 0.5.2 
## ✔ purrr   1.0.0      
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library(lmboot)
## Warning: package 'lmboot' was built under R version 4.2.3
library(caret)
## Loading required package: lattice
## 
## Attaching package: 'lattice'
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## The following object is masked from 'package:boot':
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## Attaching package: 'caret'
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##     lift
library(naniar)
library(utils)
library(stats)
library(corrplot)
## Warning: package 'corrplot' was built under R version 4.2.3
## corrplot 0.92 loaded
library(ISLR)
## Warning: package 'ISLR' was built under R version 4.2.3
library(car)
## Loading required package: carData
## 
## Attaching package: 'car'
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library(olsrr)
## Warning: package 'olsrr' was built under R version 4.2.3
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## Attaching package: 'olsrr'
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## The following object is masked from 'package:datasets':
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##     rivers

##Reading in Dataset

life = read.csv('https://github.com/athibeaux/MSDS-DS6372/raw/main/Life_Expectancy.csv')
ggplot(data = life) + geom_point(mapping = aes(x = GDP, y = Life.expectancy))
## Warning: Removed 453 rows containing missing values (`geom_point()`).

##Upon looking at the graph of the original data set, it appears that there needs to be a log transformation on the X or the GDP as we are interested in seeing the relation between Life Expenctancy and GDP.

##Checking Data Types

str(life)
## 'data.frame':    2938 obs. of  22 variables:
##  $ Country                        : chr  "Afghanistan" "Afghanistan" "Afghanistan" "Afghanistan" ...
##  $ Year                           : int  2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 ...
##  $ Status                         : chr  "Developing" "Developing" "Developing" "Developing" ...
##  $ Life.expectancy                : num  65 59.9 59.9 59.5 59.2 58.8 58.6 58.1 57.5 57.3 ...
##  $ Adult.Mortality                : int  263 271 268 272 275 279 281 287 295 295 ...
##  $ infant.deaths                  : int  62 64 66 69 71 74 77 80 82 84 ...
##  $ Alcohol                        : num  0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.03 0.02 0.03 ...
##  $ percentage.expenditure         : num  71.3 73.5 73.2 78.2 7.1 ...
##  $ Hepatitis.B                    : int  65 62 64 67 68 66 63 64 63 64 ...
##  $ Measles                        : int  1154 492 430 2787 3013 1989 2861 1599 1141 1990 ...
##  $ BMI                            : num  19.1 18.6 18.1 17.6 17.2 16.7 16.2 15.7 15.2 14.7 ...
##  $ under.five.deaths              : int  83 86 89 93 97 102 106 110 113 116 ...
##  $ Polio                          : int  6 58 62 67 68 66 63 64 63 58 ...
##  $ Total.expenditure              : num  8.16 8.18 8.13 8.52 7.87 9.2 9.42 8.33 6.73 7.43 ...
##  $ Diphtheria                     : int  65 62 64 67 68 66 63 64 63 58 ...
##  $ HIV.AIDS                       : num  0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ...
##  $ GDP                            : num  584.3 612.7 631.7 670 63.5 ...
##  $ Population                     : num  33736494 327582 31731688 3696958 2978599 ...
##  $ thinness..1.19.years           : num  17.2 17.5 17.7 17.9 18.2 18.4 18.6 18.8 19 19.2 ...
##  $ thinness.5.9.years             : num  17.3 17.5 17.7 18 18.2 18.4 18.7 18.9 19.1 19.3 ...
##  $ Income.composition.of.resources: num  0.479 0.476 0.47 0.463 0.454 0.448 0.434 0.433 0.415 0.405 ...
##  $ Schooling                      : num  10.1 10 9.9 9.8 9.5 9.2 8.9 8.7 8.4 8.1 ...
vis_miss(life)
## Warning: `gather_()` was deprecated in tidyr 1.2.0.
## ℹ Please use `gather()` instead.
## ℹ The deprecated feature was likely used in the visdat package.
##   Please report the issue at <]8;;https://github.com/ropensci/visdat/issueshttps://github.com/ropensci/visdat/issues]8;;>.

dim(life)
## [1] 2938   22

#Imputing using Median

#GDP 15% [17]  keep GDP to have it Imputed even if quite high percentage, assuming it is crucial to predicting Life.expectancy as richer countries have better health access/Medicine and tech. The numbers appear to be GDP per capita which helps as it addresses GDP/Population. GDP per Capita and Population would be too closely related and prob attribute to covariance.  

#Adjusting text angle to vis_miss
imputeMedian= preProcess(life[,-c(1:4,9)],method="medianImpute") #predictors 1:3, 9, 17 and response is 4
cleandataMedian = predict(imputeMedian,newdata=life)
dim(cleandataMedian)
## [1] 2938   22
vis_miss(cleandataMedian) + theme(axis.text.x = element_text(angle = 90, hjust = 0))

#Literature says that over 10% missing data can contribute to bias 
#HepatitsB [9] at 19% , Population 22% [18]. 
#Removing columns 9 and 18
cleandataMedian = cleandataMedian[,-c(18,9)]
vis_miss(cleandataMedian) + theme(axis.text.x = element_text(angle = 90, hjust = 0))

#removing last NA
cleandataMedian = na.omit(cleandataMedian)
vis_miss(cleandataMedian) + theme(axis.text.x = element_text(angle = 90, hjust = 0))

Splitting the data

set.seed(1234)
trainIndex<-createDataPartition(cleandataMedian$Life.expectancy,p=.8,list=F)  #p: proportion of data in train

training<-cleandataMedian[trainIndex,]
validate<-cleandataMedian[-trainIndex,]

Before and after log transforming GDP, with cleandataMedian:

ggplot(data = training) + geom_point(mapping = aes(x = GDP, y = Life.expectancy))

#Log transformation on GDP 
ggplot(data = training) + geom_point(mapping = aes(x = log(GDP), y = Life.expectancy))

##Correlation Matrix:

cor <- cor(training[,c(4,5:20)])
corrplot(cor, method = "square",  tl.srt = 50, tl.col = "black", tl.cex = 0.6, title = "Correlation of Variables", mar=c(0,0,1,0))

GGPairs:

#commented out for knitting
#ggpairs(training[,4:20])

Create categorical variable from year:

summary(training$Year)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2000    2004    2008    2008    2011    2015
#Labeled the breaks in years into 2 year buckets
training$DualYears <- cut(as.numeric(training$Year), breaks=c(0, 2001, 2003, 2005, 2007, 2009, 2011, 2013, 2015), labels=c('2000-2001', '2002-2003', '2004-2005', '2006-2007', '2008-2009', '2010-2011','2012-2013','2014-2015'))

training %>% ggplot() + geom_bar(aes(x = DualYears))

summary(training$DualYears)
## 2000-2001 2002-2003 2004-2005 2006-2007 2008-2009 2010-2011 2012-2013 2014-2015 
##       278       298       302       288       302       296       291       289

Full Model

full.model <- lm(Life.expectancy~Status + Adult.Mortality + infant.deaths + 
                   Alcohol + percentage.expenditure + Measles + BMI + 
                   under.five.deaths + Polio + Total.expenditure + 
                   Diphtheria + HIV.AIDS + log(GDP) + 
                   thinness..1.19.years + thinness.5.9.years +
                   Income.composition.of.resources + Schooling, training)

summary(full.model)
## 
## Call:
## lm(formula = Life.expectancy ~ Status + Adult.Mortality + infant.deaths + 
##     Alcohol + percentage.expenditure + Measles + BMI + under.five.deaths + 
##     Polio + Total.expenditure + Diphtheria + HIV.AIDS + log(GDP) + 
##     thinness..1.19.years + thinness.5.9.years + Income.composition.of.resources + 
##     Schooling, data = training)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -20.7738  -2.1414   0.0039   2.4033  16.0974 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      5.387e+01  7.836e-01  68.743  < 2e-16 ***
## StatusDeveloping                -1.622e+00  2.978e-01  -5.446 5.70e-08 ***
## Adult.Mortality                 -2.040e-02  8.881e-04 -22.969  < 2e-16 ***
## infant.deaths                    1.006e-01  9.196e-03  10.944  < 2e-16 ***
## Alcohol                          4.337e-02  2.924e-02   1.484   0.1381    
## percentage.expenditure           1.292e-04  5.552e-05   2.327   0.0201 *  
## Measles                         -1.809e-05  8.442e-06  -2.143   0.0322 *  
## BMI                              4.194e-02  5.581e-03   7.514 8.15e-14 ***
## under.five.deaths               -7.508e-02  6.791e-03 -11.056  < 2e-16 ***
## Polio                            2.313e-02  4.947e-03   4.676 3.10e-06 ***
## Total.expenditure                7.527e-02  3.780e-02   1.991   0.0466 *  
## Diphtheria                       3.646e-02  4.981e-03   7.319 3.41e-13 ***
## HIV.AIDS                        -4.456e-01  1.984e-02 -22.460  < 2e-16 ***
## log(GDP)                         3.807e-01  6.925e-02   5.497 4.28e-08 ***
## thinness..1.19.years            -1.105e-01  5.534e-02  -1.997   0.0459 *  
## thinness.5.9.years               4.933e-02  5.463e-02   0.903   0.3666    
## Income.composition.of.resources  5.356e+00  7.276e-01   7.362 2.50e-13 ***
## Schooling                        6.498e-01  4.849e-02  13.399  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.036 on 2326 degrees of freedom
## Multiple R-squared:  0.8209, Adjusted R-squared:  0.8196 
## F-statistic: 627.2 on 17 and 2326 DF,  p-value: < 2.2e-16
plot(full.model)

vif(full.model)
##                          Status                 Adult.Mortality 
##                        1.838844                        1.780353 
##                   infant.deaths                         Alcohol 
##                      169.796757                        1.852065 
##          percentage.expenditure                         Measles 
##                        1.662750                        1.413270 
##                             BMI               under.five.deaths 
##                        1.759970                      172.441705 
##                           Polio               Total.expenditure 
##                        1.990509                        1.193206 
##                      Diphtheria                        HIV.AIDS 
##                        2.026188                        1.470530 
##                        log(GDP)            thinness..1.19.years 
##                        2.064070                        8.502120 
##              thinness.5.9.years Income.composition.of.resources 
##                        8.625148                        3.152621 
##                       Schooling 
##                        3.542768

Fitting a preliminary model of non-redundant variables

prelim.model <- lm(Life.expectancy~Alcohol + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years +
              Income.composition.of.resources + Schooling, training)

summary(prelim.model)
## 
## Call:
## lm(formula = Life.expectancy ~ Alcohol + Measles + BMI + under.five.deaths + 
##     Polio + Total.expenditure + Diphtheria + HIV.AIDS + log(GDP) + 
##     thinness..1.19.years + Income.composition.of.resources + 
##     Schooling, data = training)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -27.8833  -2.5900   0.1524   2.6914  19.4391 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      4.256e+01  6.593e-01  64.552  < 2e-16 ***
## Alcohol                          3.571e-02  3.074e-02   1.162 0.245540    
## Measles                         -1.125e-05  9.646e-06  -1.166 0.243721    
## BMI                              5.243e-02  6.327e-03   8.287  < 2e-16 ***
## under.five.deaths               -6.712e-04  7.815e-04  -0.859 0.390553    
## Polio                            2.883e-02  5.682e-03   5.075 4.19e-07 ***
## Total.expenditure                1.532e-01  4.289e-02   3.571 0.000362 ***
## Diphtheria                       4.710e-02  5.685e-03   8.285  < 2e-16 ***
## HIV.AIDS                        -6.889e-01  1.996e-02 -34.516  < 2e-16 ***
## log(GDP)                         5.889e-01  7.086e-02   8.311  < 2e-16 ***
## thinness..1.19.years            -8.489e-02  3.047e-02  -2.786 0.005385 ** 
## Income.composition.of.resources  8.038e+00  8.268e-01   9.722  < 2e-16 ***
## Schooling                        7.919e-01  5.543e-02  14.286  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.642 on 2331 degrees of freedom
## Multiple R-squared:  0.7625, Adjusted R-squared:  0.7613 
## F-statistic: 623.7 on 12 and 2331 DF,  p-value: < 2.2e-16
plot(prelim.model)

vif(prelim.model)
##                         Alcohol                         Measles 
##                        1.547310                        1.394134 
##                             BMI               under.five.deaths 
##                        1.709194                        1.725861 
##                           Polio               Total.expenditure 
##                        1.984334                        1.160591 
##                      Diphtheria                        HIV.AIDS 
##                        1.994255                        1.124632 
##                        log(GDP)            thinness..1.19.years 
##                        1.633008                        1.947947 
## Income.composition.of.resources                       Schooling 
##                        3.076060                        3.498226

Feature Selection Tools: Penalized Regression

# Penalized Regression

#Setting kfold parameters
fitControl<-trainControl(method="repeatedcv",number=5,repeats=1) 

#Fitting glmnet
set.seed(1234)
glmnet.fit<-train(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + thinness.5.9.years +
              Income.composition.of.resources + Schooling,
                  data=training,
                  method="glmnet",
                  trControl=fitControl
)

glmnet.fit
## glmnet 
## 
## 2344 samples
##   15 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1875, 1877, 1874, 1875, 1875 
## Resampling results across tuning parameters:
## 
##   alpha  lambda      RMSE      Rsquared   MAE     
##   0.10   0.01359526  4.546733  0.7715121  3.428469
##   0.10   0.13595255  4.617190  0.7645704  3.477897
##   0.10   1.35952554  4.677957  0.7611292  3.543112
##   0.55   0.01359526  4.546678  0.7715357  3.427825
##   0.55   0.13595255  4.642083  0.7621296  3.494318
##   0.55   1.35952554  4.837724  0.7583217  3.646672
##   1.00   0.01359526  4.547465  0.7714789  3.427827
##   1.00   0.13595255  4.645565  0.7619759  3.493011
##   1.00   1.35952554  5.132045  0.7483316  3.890102
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 0.55 and lambda = 0.01359526.
plot(glmnet.fit)

#Investigating coefficients
opt.pen<-glmnet.fit$finalModel$lambdaOpt #penalty term
coef(glmnet.fit$finalModel,opt.pen)
## 16 x 1 sparse Matrix of class "dgCMatrix"
##                                            s1
## (Intercept)                      4.460994e+01
## infant.deaths                    7.072859e-02
## Alcohol                          4.933926e-02
## percentage.expenditure           2.592483e-04
## Measles                         -6.563182e-06
## BMI                              5.356624e-02
## under.five.deaths               -5.267115e-02
## Polio                            2.688020e-02
## Total.expenditure                1.322282e-01
## Diphtheria                       4.334536e-02
## HIV.AIDS                        -6.760276e-01
## log(GDP)                         4.439098e-01
## thinness..1.19.years            -9.170910e-02
## thinness.5.9.years               .           
## Income.composition.of.resources  7.354446e+00
## Schooling                        7.755679e-01
glmnet.fit.model <-lm(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years +
              Income.composition.of.resources + Schooling,
          data=training)

plot(glmnet.fit.model)

#Lets force a LASSO model and add complexity
set.seed(1234)
glmnet.fit2<-train(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + poly(Polio,2) + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + thinness.5.9.years +
              Income.composition.of.resources + Schooling,
                  data=training,
                  method="glmnet",
                  trControl=fitControl,
                  tuneGrid=expand.grid(data.frame(alpha=1,lambda=seq(0,.05,.001)))
)

glmnet.fit2
## glmnet 
## 
## 2344 samples
##   15 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1875, 1877, 1874, 1875, 1875 
## Resampling results across tuning parameters:
## 
##   lambda  RMSE      Rsquared   MAE     
##   0.000   4.438996  0.7821622  3.353113
##   0.001   4.438996  0.7821622  3.353113
##   0.002   4.439178  0.7821469  3.353265
##   0.003   4.439604  0.7821102  3.353665
##   0.004   4.439905  0.7820844  3.354178
##   0.005   4.440391  0.7820411  3.354927
##   0.006   4.441047  0.7819817  3.355913
##   0.007   4.441877  0.7819056  3.356904
##   0.008   4.442881  0.7818127  3.357980
##   0.009   4.444052  0.7817038  3.359160
##   0.010   4.445390  0.7815786  3.360345
##   0.011   4.446942  0.7814329  3.361585
##   0.012   4.448665  0.7812705  3.362960
##   0.013   4.450543  0.7810932  3.364494
##   0.014   4.452643  0.7808933  3.366372
##   0.015   4.454931  0.7806745  3.368319
##   0.016   4.457387  0.7804391  3.370265
##   0.017   4.460005  0.7801876  3.372391
##   0.018   4.462793  0.7799192  3.374614
##   0.019   4.465766  0.7796322  3.376937
##   0.020   4.468895  0.7793297  3.379295
##   0.021   4.472143  0.7790153  3.381720
##   0.022   4.475542  0.7786857  3.384205
##   0.023   4.479080  0.7783420  3.386881
##   0.024   4.482819  0.7779772  3.389618
##   0.025   4.486731  0.7775947  3.392610
##   0.026   4.490825  0.7771933  3.395700
##   0.027   4.495096  0.7767735  3.398865
##   0.028   4.499526  0.7763374  3.402101
##   0.029   4.504118  0.7758847  3.405358
##   0.030   4.508868  0.7754155  3.408641
##   0.031   4.513601  0.7749468  3.411809
##   0.032   4.517809  0.7745270  3.414992
##   0.033   4.522146  0.7740937  3.418897
##   0.034   4.526346  0.7736733  3.422622
##   0.035   4.529756  0.7733298  3.425748
##   0.036   4.533274  0.7729749  3.428874
##   0.037   4.536688  0.7726295  3.431850
##   0.038   4.538484  0.7724495  3.433561
##   0.039   4.539767  0.7723218  3.434705
##   0.040   4.541073  0.7721918  3.435852
##   0.041   4.542062  0.7720926  3.436751
##   0.042   4.542531  0.7720457  3.437187
##   0.043   4.542508  0.7720491  3.437149
##   0.044   4.542487  0.7720524  3.437110
##   0.045   4.542467  0.7720556  3.437071
##   0.046   4.542450  0.7720586  3.437032
##   0.047   4.542435  0.7720615  3.436993
##   0.048   4.542421  0.7720644  3.436953
##   0.049   4.542409  0.7720671  3.436915
##   0.050   4.542399  0.7720696  3.436881
## 
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.001.
plot(glmnet.fit2)

opt.pen<-glmnet.fit2$finalModel$lambdaOpt   #penalty term
coef(glmnet.fit2$finalModel,opt.pen)
## 17 x 1 sparse Matrix of class "dgCMatrix"
##                                            s1
## (Intercept)                      5.044976e+01
## infant.deaths                    1.003575e-01
## Alcohol                          4.928420e-02
## percentage.expenditure           3.159795e-04
## Measles                         -3.689026e-06
## BMI                              5.226929e-02
## under.five.deaths               -7.357662e-02
## poly(Polio, 2)1                  5.473565e+01
## poly(Polio, 2)2                  5.245271e+01
## Total.expenditure                1.330491e-01
## Diphtheria                       2.136060e-02
## HIV.AIDS                        -6.514221e-01
## log(GDP)                         3.653079e-01
## thinness..1.19.years            -1.069419e-01
## thinness.5.9.years               .           
## Income.composition.of.resources  6.837594e+00
## Schooling                        7.006484e-01
# Different way to do GLMNET

x=model.matrix(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + thinness.5.9.years +
              Income.composition.of.resources + Schooling,
               training)[,-1]
y=log(training$Life.expectancy)

library(glmnet)
## Warning: package 'glmnet' was built under R version 4.2.3
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## Loaded glmnet 4.1-7
set.seed(1234)

grid=10^seq(10,-2, length =100)
lasso.mod=glmnet(x,y,alpha=1, lambda =grid)

cv.out=cv.glmnet(x,y,alpha=1)
plot(cv.out)

bestlambda<-cv.out$lambda.1se
coef(cv.out,s=bestlambda)
## 16 x 1 sparse Matrix of class "dgCMatrix"
##                                            s1
## (Intercept)                      3.844715e+00
## infant.deaths                    3.126175e-04
## Alcohol                          1.412272e-04
## percentage.expenditure           2.088892e-06
## Measles                         -2.066844e-07
## BMI                              8.656727e-04
## under.five.deaths               -2.420026e-04
## Polio                            4.313928e-04
## Total.expenditure                1.324203e-03
## Diphtheria                       7.540932e-04
## HIV.AIDS                        -1.150787e-02
## log(GDP)                         6.791475e-03
## thinness..1.19.years            -8.147405e-04
## thinness.5.9.years               .           
## Income.composition.of.resources  1.152774e-01
## Schooling                        1.190970e-02

Feature Selection Tools: Forward Selection

fwd.selection = lm(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + thinness.5.9.years +
              Income.composition.of.resources + Schooling, data = training)

# Forward
ols_step_forward_p(fwd.selection, penter = 0.05, details = TRUE)
## Forward Selection Method    
## ---------------------------
## 
## Candidate Terms: 
## 
## 1. infant.deaths 
## 2. Alcohol 
## 3. percentage.expenditure 
## 4. Measles 
## 5. BMI 
## 6. under.five.deaths 
## 7. Polio 
## 8. Total.expenditure 
## 9. Diphtheria 
## 10. HIV.AIDS 
## 11. log(GDP) 
## 12. thinness..1.19.years 
## 13. thinness.5.9.years 
## 14. Income.composition.of.resources 
## 15. Schooling 
## 
## We are selecting variables based on p value...
## 
## 
## Forward Selection: Step 1 
## 
## - Schooling 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.742       RMSE                6.376 
## R-Squared               0.550       Coef. Var           9.217 
## Adj. R-Squared          0.550       MSE                40.657 
## Pred R-Squared          0.548       MAE                 4.522 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                    
## --------------------------------------------------------------------------
##                   Sum of                                                  
##                  Squares          DF    Mean Square       F          Sig. 
## --------------------------------------------------------------------------
## Regression    116351.776           2      58175.888    1430.894    0.0000 
## Residual       95178.071        2341         40.657                       
## Total         211529.848        2343                                      
## --------------------------------------------------------------------------
## 
##                                             Parameter Estimates                                              
## ------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta      t        Sig      lower     upper 
## ------------------------------------------------------------------------------------------------------------
##                     (Intercept)    43.597         0.507                 86.019    0.000    42.603    44.591 
## Income.composition.of.resources    15.377         1.093        0.329    14.063    0.000    13.233    17.521 
##                       Schooling     1.322         0.069        0.450    19.231    0.000     1.187     1.457 
## ------------------------------------------------------------------------------------------------------------
## 
## 
## 
## Forward Selection: Step 2 
## 
## - HIV.AIDS 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.838       RMSE                5.191 
## R-Squared               0.702       Coef. Var           7.504 
## Adj. R-Squared          0.702       MSE                26.948 
## Pred R-Squared          0.700       MAE                 3.727 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                    
## --------------------------------------------------------------------------
##                   Sum of                                                  
##                  Squares          DF    Mean Square       F          Sig. 
## --------------------------------------------------------------------------
## Regression    148470.718           3      49490.239    1836.485    0.0000 
## Residual       63059.129        2340         26.948                       
## Total         211529.848        2343                                      
## --------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    48.062         0.432                 111.146    0.000    47.214    48.910 
## Income.composition.of.resources    11.453         0.897        0.245     12.762    0.000     9.693    13.213 
##                       Schooling     1.267         0.056        0.431     22.619    0.000     1.157     1.376 
##                        HIV.AIDS    -0.750         0.022       -0.402    -34.523    0.000    -0.793    -0.707 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## Forward Selection: Step 3 
## 
## - Diphtheria 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.855       RMSE                4.931 
## R-Squared               0.731       Coef. Var           7.128 
## Adj. R-Squared          0.731       MSE                24.314 
## Pred R-Squared          0.729       MAE                 3.605 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                    
## --------------------------------------------------------------------------
##                   Sum of                                                  
##                  Squares          DF    Mean Square       F          Sig. 
## --------------------------------------------------------------------------
## Regression    154658.745           4      38664.686    1590.205    0.0000 
## Residual       56871.102        2339         24.314                       
## Total         211529.848        2343                                      
## --------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    44.282         0.474                  93.387    0.000    43.352    45.212 
## Income.composition.of.resources    10.312         0.855        0.221     12.055    0.000     8.635    11.989 
##                       Schooling     1.129         0.054        0.385     20.962    0.000     1.024     1.235 
##                        HIV.AIDS    -0.722         0.021       -0.387    -34.868    0.000    -0.763    -0.682 
##                      Diphtheria     0.074         0.005        0.186     15.953    0.000     0.065     0.083 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## Forward Selection: Step 4 
## 
## - BMI 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.865       RMSE                4.776 
## R-Squared               0.748       Coef. Var           6.904 
## Adj. R-Squared          0.747       MSE                22.813 
## Pred R-Squared          0.746       MAE                 3.544 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                    
## --------------------------------------------------------------------------
##                   Sum of                                                  
##                  Squares          DF    Mean Square       F          Sig. 
## --------------------------------------------------------------------------
## Regression    158193.664           5      31638.733    1386.889    0.0000 
## Residual       53336.184        2338         22.813                       
## Total         211529.848        2343                                      
## --------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    44.336         0.459                  96.525    0.000    43.435    45.237 
## Income.composition.of.resources     9.331         0.832        0.200     11.211    0.000     7.699    10.963 
##                       Schooling     0.970         0.054        0.330     18.043    0.000     0.864     1.075 
##                        HIV.AIDS    -0.690         0.020       -0.370    -34.134    0.000    -0.730    -0.651 
##                      Diphtheria     0.069         0.005        0.174     15.309    0.000     0.060     0.078 
##                             BMI     0.074         0.006        0.154     12.448    0.000     0.062     0.086 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## Forward Selection: Step 5 
## 
## - log(GDP) 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.869       RMSE                4.704 
## R-Squared               0.756       Coef. Var           6.799 
## Adj. R-Squared          0.755       MSE                22.125 
## Pred R-Squared          0.753       MAE                 3.506 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                    
## --------------------------------------------------------------------------
##                   Sum of                                                  
##                  Squares          DF    Mean Square       F          Sig. 
## --------------------------------------------------------------------------
## Regression    159823.821           6      26637.303    1203.948    0.0000 
## Residual       51706.027        2337         22.125                       
## Total         211529.848        2343                                      
## --------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    42.099         0.522                  80.644    0.000    41.076    43.123 
## Income.composition.of.resources     8.057         0.833        0.173      9.672    0.000     6.424     9.691 
##                       Schooling     0.872         0.054        0.297     16.098    0.000     0.765     0.978 
##                        HIV.AIDS    -0.686         0.020       -0.368    -34.417    0.000    -0.725    -0.647 
##                      Diphtheria     0.068         0.004        0.171     15.333    0.000     0.060     0.077 
##                             BMI     0.067         0.006        0.140     11.352    0.000     0.055     0.079 
##                        log(GDP)     0.610         0.071        0.111      8.584    0.000     0.471     0.749 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## Forward Selection: Step 6 
## 
## - Polio 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.871       RMSE                4.679 
## R-Squared               0.758       Coef. Var           6.763 
## Adj. R-Squared          0.758       MSE                21.889 
## Pred R-Squared          0.756       MAE                 3.491 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                    
## --------------------------------------------------------------------------
##                   Sum of                                                  
##                  Squares          DF    Mean Square       F          Sig. 
## --------------------------------------------------------------------------
## Regression    160397.905           7      22913.986    1046.842    0.0000 
## Residual       51131.943        2336         21.889                       
## Total         211529.848        2343                                      
## --------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    41.581         0.529                  78.597    0.000    40.543    42.618 
## Income.composition.of.resources     7.914         0.829        0.169      9.546    0.000     6.288     9.540 
##                       Schooling     0.855         0.054        0.291     15.850    0.000     0.749     0.961 
##                        HIV.AIDS    -0.683         0.020       -0.367    -34.475    0.000    -0.722    -0.644 
##                      Diphtheria     0.050         0.006        0.125      8.740    0.000     0.039     0.061 
##                             BMI     0.066         0.006        0.137     11.195    0.000     0.054     0.077 
##                        log(GDP)     0.604         0.071        0.110      8.539    0.000     0.465     0.742 
##                           Polio     0.029         0.006        0.073      5.121    0.000     0.018     0.041 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## Forward Selection: Step 7 
## 
## - percentage.expenditure 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.872       RMSE                4.657 
## R-Squared               0.761       Coef. Var           6.732 
## Adj. R-Squared          0.760       MSE                21.689 
## Pred R-Squared          0.758       MAE                 3.479 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                   
## -------------------------------------------------------------------------
##                   Sum of                                                 
##                  Squares          DF    Mean Square       F         Sig. 
## -------------------------------------------------------------------------
## Regression    160886.865           8      20110.858    927.253    0.0000 
## Residual       50642.982        2335         21.689                      
## Total         211529.848        2343                                     
## -------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    42.827         0.588                  72.787    0.000    41.673    43.980 
## Income.composition.of.resources     7.810         0.826        0.167      9.460    0.000     6.191     9.429 
##                       Schooling     0.839         0.054        0.286     15.592    0.000     0.733     0.944 
##                        HIV.AIDS    -0.685         0.020       -0.367    -34.709    0.000    -0.724    -0.646 
##                      Diphtheria     0.050         0.006        0.127      8.882    0.000     0.039     0.062 
##                             BMI     0.067         0.006        0.139     11.403    0.000     0.055     0.078 
##                        log(GDP)     0.431         0.079        0.078      5.441    0.000     0.276     0.586 
##                           Polio     0.029         0.006        0.074      5.161    0.000     0.018     0.041 
##          percentage.expenditure     0.000         0.000        0.059      4.748    0.000     0.000     0.000 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## Forward Selection: Step 8 
## 
## - thinness..1.19.years 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.873       RMSE                4.640 
## R-Squared               0.762       Coef. Var           6.707 
## Adj. R-Squared          0.762       MSE                21.527 
## Pred R-Squared          0.760       MAE                 3.481 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                   
## -------------------------------------------------------------------------
##                   Sum of                                                 
##                  Squares          DF    Mean Square       F         Sig. 
## -------------------------------------------------------------------------
## Regression    161286.681           9      17920.742    832.492    0.0000 
## Residual       50243.166        2334         21.527                      
## Total         211529.848        2343                                     
## -------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    44.180         0.665                  66.433    0.000    42.876    45.484 
## Income.composition.of.resources     7.719         0.823        0.165      9.382    0.000     6.105     9.332 
##                       Schooling     0.814         0.054        0.277     15.106    0.000     0.709     0.920 
##                        HIV.AIDS    -0.680         0.020       -0.364    -34.497    0.000    -0.718    -0.641 
##                      Diphtheria     0.050         0.006        0.125      8.769    0.000     0.039     0.061 
##                             BMI     0.057         0.006        0.118      8.989    0.000     0.044     0.069 
##                        log(GDP)     0.433         0.079        0.079      5.483    0.000     0.278     0.588 
##                           Polio     0.029         0.006        0.074      5.188    0.000     0.018     0.041 
##          percentage.expenditure     0.000         0.000        0.055      4.437    0.000     0.000     0.000 
##            thinness..1.19.years    -0.115         0.027       -0.053     -4.310    0.000    -0.168    -0.063 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## Forward Selection: Step 9 
## 
## - Total.expenditure 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.874       RMSE                4.629 
## R-Squared               0.764       Coef. Var           6.691 
## Adj. R-Squared          0.763       MSE                21.428 
## Pred R-Squared          0.761       MAE                 3.474 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                   
## -------------------------------------------------------------------------
##                   Sum of                                                 
##                  Squares          DF    Mean Square       F         Sig. 
## -------------------------------------------------------------------------
## Regression    161538.357          10      16153.836    753.866    0.0000 
## Residual       49991.490        2333         21.428                      
## Total         211529.848        2343                                     
## -------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    43.422         0.699                  62.084    0.000    42.051    44.794 
## Income.composition.of.resources     7.910         0.823        0.169      9.615    0.000     6.297     9.524 
##                       Schooling     0.795         0.054        0.271     14.704    0.000     0.689     0.901 
##                        HIV.AIDS    -0.685         0.020       -0.367    -34.741    0.000    -0.724    -0.646 
##                      Diphtheria     0.049         0.006        0.122      8.580    0.000     0.037     0.060 
##                             BMI     0.054         0.006        0.113      8.631    0.000     0.042     0.067 
##                        log(GDP)     0.454         0.079        0.083      5.751    0.000     0.299     0.609 
##                           Polio     0.029         0.006        0.073      5.177    0.000     0.018     0.040 
##          percentage.expenditure     0.000         0.000        0.051      4.029    0.000     0.000     0.000 
##            thinness..1.19.years    -0.102         0.027       -0.047     -3.795    0.000    -0.155    -0.049 
##               Total.expenditure     0.145         0.042        0.037      3.427    0.001     0.062     0.228 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## No more variables to be added.
## 
## Variables Entered: 
## 
## + Income.composition.of.resources 
## + Schooling 
## + HIV.AIDS 
## + Diphtheria 
## + BMI 
## + log(GDP) 
## + Polio 
## + percentage.expenditure 
## + thinness..1.19.years 
## + Total.expenditure 
## 
## 
## Final Model Output 
## ------------------
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.874       RMSE                4.629 
## R-Squared               0.764       Coef. Var           6.691 
## Adj. R-Squared          0.763       MSE                21.428 
## Pred R-Squared          0.761       MAE                 3.474 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                   
## -------------------------------------------------------------------------
##                   Sum of                                                 
##                  Squares          DF    Mean Square       F         Sig. 
## -------------------------------------------------------------------------
## Regression    161538.357          10      16153.836    753.866    0.0000 
## Residual       49991.490        2333         21.428                      
## Total         211529.848        2343                                     
## -------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    43.422         0.699                  62.084    0.000    42.051    44.794 
## Income.composition.of.resources     7.910         0.823        0.169      9.615    0.000     6.297     9.524 
##                       Schooling     0.795         0.054        0.271     14.704    0.000     0.689     0.901 
##                        HIV.AIDS    -0.685         0.020       -0.367    -34.741    0.000    -0.724    -0.646 
##                      Diphtheria     0.049         0.006        0.122      8.580    0.000     0.037     0.060 
##                             BMI     0.054         0.006        0.113      8.631    0.000     0.042     0.067 
##                        log(GDP)     0.454         0.079        0.083      5.751    0.000     0.299     0.609 
##                           Polio     0.029         0.006        0.073      5.177    0.000     0.018     0.040 
##          percentage.expenditure     0.000         0.000        0.051      4.029    0.000     0.000     0.000 
##            thinness..1.19.years    -0.102         0.027       -0.047     -3.795    0.000    -0.155    -0.049 
##               Total.expenditure     0.145         0.042        0.037      3.427    0.001     0.062     0.228 
## -------------------------------------------------------------------------------------------------------------
## 
##                                          Selection Summary                                           
## ----------------------------------------------------------------------------------------------------
##         Variable                                         Adj.                                           
## Step                Entered                R-Square    R-Square      C(p)          AIC         RMSE     
## ----------------------------------------------------------------------------------------------------
##    1    Income.composition.of.resources      0.5500      0.5497    2327.9505    15341.9036    6.3763    
##    2    Schooling                            0.7019      0.7015     755.3715    14378.9334    5.1912    
##    3    HIV.AIDS                             0.7311      0.7307     454.0135    14138.8322    4.9310    
##    4    Diphtheria                           0.7479      0.7473     282.7199    13990.4121    4.7763    
##    5    BMI                                  0.7556      0.7549     204.8041    13919.6529    4.7037    
##    6    log(GDP)                             0.7583      0.7576     178.6605    13895.4823    4.6785    
##    7    Polio                                0.7606      0.7598     156.6900    13874.9594    4.6571    
##    8    percentage.expenditure               0.7625      0.7616     139.0897    13858.3806    4.6397    
##    9    thinness..1.19.years                 0.7637      0.7627     128.7517    13848.6096    4.6290    
##   10    Total.expenditure                        NA          NA           NA            NA        NA    
## ----------------------------------------------------------------------------------------------------
# Forward Selection Chosen Model

fwd.select.model <- lm(Life.expectancy~ Income.composition.of.resources + Schooling +
                         HIV.AIDS + Diphtheria +
                         BMI + log(GDP) + Polio +
                         percentage.expenditure + thinness..1.19.years + Total.expenditure, training)

plot(fwd.select.model)

library(leaps)
## Warning: package 'leaps' was built under R version 4.2.3
reg.fwd=regsubsets(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + thinness.5.9.years +
              Income.composition.of.resources + Schooling,
                   data=training,method="forward",nvmax=15)

summary(reg.fwd)$adjr2
##  [1] 0.5118279 0.6808674 0.7140742 0.7338469 0.7473158 0.7549340 0.7575512
##  [8] 0.7597668 0.7615613 0.7626540 0.7628746 0.7628610 0.7737752 0.7741531
## [15] 0.7740578
summary(reg.fwd)$rss
##  [1] 103218.90  67448.44  60404.40  56203.20  53336.18  51706.03  51131.94
##  [8]  50642.98  50243.17  49991.49  49923.61  49905.07  47587.78  47487.89
## [15]  47487.55
summary(reg.fwd)$bic
##  [1] -1666.334 -2655.919 -2906.706 -3067.922 -3182.891 -3247.891 -3266.302
##  [8] -3281.065 -3291.884 -3295.895 -3291.321 -3284.432 -3388.122 -3385.287
## [15] -3377.544
par(mfrow=c(1,3))
bics<-summary(reg.fwd)$bic
plot(1:15,bics,type="l",ylab="BIC",xlab="# of predictors")
index<-which(bics==min(bics))
points(index,bics[index],col="red",pch=10)

adjr2<-summary(reg.fwd)$adjr2
plot(1:15,adjr2,type="l",ylab="Adjusted R-squared",xlab="# of predictors")
index<-which(adjr2==max(adjr2))
points(index,adjr2[index],col="red",pch=10)

rss<-summary(reg.fwd)$rss
plot(1:15,rss,type="l",ylab="train RSS",xlab="# of predictors")
index<-which(rss==min(rss))
points(index,rss[index],col="red",pch=10)

Backward Selection

bck.selection = lm(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + thinness.5.9.years +
              Income.composition.of.resources + Schooling, data = training)

# Backward
ols_step_backward_p(bck.selection, prem = 0.05, details = TRUE)
## Backward Elimination Method 
## ---------------------------
## 
## Candidate Terms: 
## 
## 1 . infant.deaths 
## 2 . Alcohol 
## 3 . percentage.expenditure 
## 4 . Measles 
## 5 . BMI 
## 6 . under.five.deaths 
## 7 . Polio 
## 8 . Total.expenditure 
## 9 . Diphtheria 
## 10 . HIV.AIDS 
## 11 . log(GDP) 
## 12 . thinness..1.19.years 
## 13 . thinness.5.9.years 
## 14 . Income.composition.of.resources 
## 15 . Schooling 
## 
## We are eliminating variables based on p value...
## 
## - thinness.5.9.years 
## 
## Backward Elimination: Step 1 
## 
##  Variable thinness.5.9.years Removed 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.881       RMSE                4.516 
## R-Squared               0.776       Coef. Var           6.527 
## Adj. R-Squared          0.774       MSE                20.390 
## Pred R-Squared          0.771       MAE                 3.389 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                   
## -------------------------------------------------------------------------
##                   Sum of                                                 
##                  Squares          DF    Mean Square       F         Sig. 
## -------------------------------------------------------------------------
## Regression    164041.953          14      11717.282    574.663    0.0000 
## Residual       47487.895        2329         20.390                      
## Total         211529.848        2343                                     
## -------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    45.159         0.702                  64.284    0.000    43.781    46.536 
##                   infant.deaths     0.112         0.010        1.387     10.864    0.000     0.091     0.132 
##                         Alcohol     0.067         0.030        0.027      2.213    0.027     0.008     0.127 
##          percentage.expenditure     0.000         0.000        0.055      4.452    0.000     0.000     0.000 
##                         Measles     0.000         0.000       -0.005     -0.419    0.675     0.000     0.000 
##                             BMI     0.053         0.006        0.111      8.655    0.000     0.041     0.065 
##               under.five.deaths    -0.083         0.008       -1.404    -10.912    0.000    -0.098    -0.068 
##                           Polio     0.026         0.006        0.065      4.670    0.000     0.015     0.037 
##               Total.expenditure     0.132         0.042        0.034      3.160    0.002     0.050     0.215 
##                      Diphtheria     0.041         0.006        0.103      7.341    0.000     0.030     0.052 
##                        HIV.AIDS    -0.671         0.019       -0.360    -34.460    0.000    -0.710    -0.633 
##                        log(GDP)     0.443         0.077        0.081      5.723    0.000     0.291     0.594 
##            thinness..1.19.years    -0.096         0.030       -0.044     -3.233    0.001    -0.154    -0.038 
## Income.composition.of.resources     7.023         0.809        0.150      8.681    0.000     5.436     8.609 
##                       Schooling     0.768         0.054        0.262     14.235    0.000     0.662     0.874 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## - Measles 
## 
## Backward Elimination: Step 2 
## 
##  Variable Measles Removed 
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.881       RMSE                4.515 
## R-Squared               0.775       Coef. Var           6.526 
## Adj. R-Squared          0.774       MSE                20.383 
## Pred R-Squared          0.772       MAE                 3.389 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                   
## -------------------------------------------------------------------------
##                   Sum of                                                 
##                  Squares          DF    Mean Square       F         Sig. 
## -------------------------------------------------------------------------
## Regression    164038.369          13      12618.336    619.074    0.0000 
## Residual       47491.479        2330         20.383                      
## Total         211529.848        2343                                     
## -------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    45.142         0.701                  64.370    0.000    43.767    46.518 
##                   infant.deaths     0.112         0.010        1.391     10.919    0.000     0.092     0.132 
##                         Alcohol     0.067         0.030        0.027      2.208    0.027     0.007     0.127 
##          percentage.expenditure     0.000         0.000        0.055      4.459    0.000     0.000     0.000 
##                             BMI     0.054         0.006        0.112      8.710    0.000     0.042     0.066 
##               under.five.deaths    -0.083         0.008       -1.411    -11.035    0.000    -0.098    -0.068 
##                           Polio     0.026         0.006        0.065      4.667    0.000     0.015     0.037 
##               Total.expenditure     0.133         0.042        0.034      3.185    0.001     0.051     0.215 
##                      Diphtheria     0.041         0.006        0.103      7.348    0.000     0.030     0.052 
##                        HIV.AIDS    -0.671         0.019       -0.360    -34.464    0.000    -0.709    -0.633 
##                        log(GDP)     0.442         0.077        0.080      5.719    0.000     0.290     0.594 
##            thinness..1.19.years    -0.095         0.030       -0.044     -3.212    0.001    -0.153    -0.037 
## Income.composition.of.resources     7.035         0.808        0.151      8.704    0.000     5.450     8.620 
##                       Schooling     0.767         0.054        0.261     14.231    0.000     0.662     0.873 
## -------------------------------------------------------------------------------------------------------------
## 
## 
## 
## No more variables satisfy the condition of p value = 0.05
## 
## 
## Variables Removed: 
## 
## - thinness.5.9.years 
## - Measles 
## 
## 
## Final Model Output 
## ------------------
## 
##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.881       RMSE                4.515 
## R-Squared               0.775       Coef. Var           6.526 
## Adj. R-Squared          0.774       MSE                20.383 
## Pred R-Squared          0.772       MAE                 3.389 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                   
## -------------------------------------------------------------------------
##                   Sum of                                                 
##                  Squares          DF    Mean Square       F         Sig. 
## -------------------------------------------------------------------------
## Regression    164038.369          13      12618.336    619.074    0.0000 
## Residual       47491.479        2330         20.383                      
## Total         211529.848        2343                                     
## -------------------------------------------------------------------------
## 
##                                              Parameter Estimates                                              
## -------------------------------------------------------------------------------------------------------------
##                           model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -------------------------------------------------------------------------------------------------------------
##                     (Intercept)    45.142         0.701                  64.370    0.000    43.767    46.518 
##                   infant.deaths     0.112         0.010        1.391     10.919    0.000     0.092     0.132 
##                         Alcohol     0.067         0.030        0.027      2.208    0.027     0.007     0.127 
##          percentage.expenditure     0.000         0.000        0.055      4.459    0.000     0.000     0.000 
##                             BMI     0.054         0.006        0.112      8.710    0.000     0.042     0.066 
##               under.five.deaths    -0.083         0.008       -1.411    -11.035    0.000    -0.098    -0.068 
##                           Polio     0.026         0.006        0.065      4.667    0.000     0.015     0.037 
##               Total.expenditure     0.133         0.042        0.034      3.185    0.001     0.051     0.215 
##                      Diphtheria     0.041         0.006        0.103      7.348    0.000     0.030     0.052 
##                        HIV.AIDS    -0.671         0.019       -0.360    -34.464    0.000    -0.709    -0.633 
##                        log(GDP)     0.442         0.077        0.080      5.719    0.000     0.290     0.594 
##            thinness..1.19.years    -0.095         0.030       -0.044     -3.212    0.001    -0.153    -0.037 
## Income.composition.of.resources     7.035         0.808        0.151      8.704    0.000     5.450     8.620 
##                       Schooling     0.767         0.054        0.261     14.231    0.000     0.662     0.873 
## -------------------------------------------------------------------------------------------------------------
## 
## 
##                                  Elimination Summary                                  
## -------------------------------------------------------------------------------------
##         Variable                            Adj.                                         
## Step         Removed          R-Square    R-Square     C(p)         AIC         RMSE     
## -------------------------------------------------------------------------------------
##    1    thinness.5.9.years      0.7755      0.7742    14.0170    13736.1797    4.5155    
##    2    Measles                 0.7755      0.7742    12.1927    13734.3566    4.5147    
## -------------------------------------------------------------------------------------
# Backward Selection Chosen Model
bck.select.model <- lm(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + 
              Income.composition.of.resources + Schooling, data = training)

plot(bck.select.model)

Stepwise Selection

sw.selection = lm(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + thinness.5.9.years +
              Income.composition.of.resources + Schooling, data = training)
summary(sw.selection)
## 
## Call:
## lm(formula = Life.expectancy ~ infant.deaths + Alcohol + percentage.expenditure + 
##     Measles + BMI + under.five.deaths + Polio + Total.expenditure + 
##     Diphtheria + HIV.AIDS + log(GDP) + thinness..1.19.years + 
##     thinness.5.9.years + Income.composition.of.resources + Schooling, 
##     data = training)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -26.0853  -2.5875   0.0947   2.6344  18.6763 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      4.515e+01  7.078e-01  63.787  < 2e-16 ***
## infant.deaths                    1.115e-01  1.028e-02  10.853  < 2e-16 ***
## Alcohol                          6.734e-02  3.040e-02   2.215  0.02686 *  
## percentage.expenditure           2.696e-04  6.057e-05   4.451 8.96e-06 ***
## Measles                         -3.885e-06  9.417e-06  -0.413  0.67999    
## BMI                              5.349e-02  6.217e-03   8.604  < 2e-16 ***
## under.five.deaths               -8.275e-02  7.588e-03 -10.906  < 2e-16 ***
## Polio                            2.584e-02  5.535e-03   4.669 3.20e-06 ***
## Total.expenditure                1.327e-01  4.197e-02   3.161  0.00159 ** 
## Diphtheria                       4.087e-02  5.571e-03   7.336 3.03e-13 ***
## HIV.AIDS                        -6.714e-01  1.951e-02 -34.419  < 2e-16 ***
## log(GDP)                         4.431e-01  7.745e-02   5.721 1.20e-08 ***
## thinness..1.19.years            -1.031e-01  6.194e-02  -1.665  0.09611 .  
## thinness.5.9.years               7.969e-03  6.110e-02   0.130  0.89624    
## Income.composition.of.resources  7.023e+00  8.091e-01   8.679  < 2e-16 ***
## Schooling                        7.680e-01  5.398e-02  14.226  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.516 on 2328 degrees of freedom
## Multiple R-squared:  0.7755, Adjusted R-squared:  0.7741 
## F-statistic: 536.1 on 15 and 2328 DF,  p-value: < 2.2e-16
# Stepwise
ols_step_both_p(sw.selection, prem = 0.05, pent = 0.05, details = FALSE)
## 
##                                            Stepwise Selection Summary                                            
## ----------------------------------------------------------------------------------------------------------------
##                                             Added/                   Adj.                                           
## Step               Variable                Removed     R-Square    R-Square      C(p)          AIC         RMSE     
## ----------------------------------------------------------------------------------------------------------------
##    1    Income.composition.of.resources    addition       0.550       0.550    2327.9510    15341.9036    6.3763    
##    2               Schooling               addition       0.702       0.702     755.3720    14378.9334    5.1912    
##    3               HIV.AIDS                addition       0.731       0.731     454.0140    14138.8322    4.9310    
##    4              Diphtheria               addition       0.748       0.747     282.7200    13990.4121    4.7763    
##    5                  BMI                  addition       0.756       0.755     204.8040    13919.6529    4.7037    
##    6               log(GDP)                addition       0.758       0.758     178.6610    13895.4823    4.6785    
##    7                 Polio                 addition       0.761       0.760     156.6900    13874.9594    4.6571    
##    8        percentage.expenditure         addition       0.762       0.762     139.0900    13858.3806    4.6397    
##    9         thinness..1.19.years          addition       0.764       0.763     128.7520    13848.6096    4.6290    
## ----------------------------------------------------------------------------------------------------------------
# Stepwise Selection Chosen Model
sw.select.model = lm(Life.expectancy~ percentage.expenditure + 
                       BMI + Polio + Diphtheria + HIV.AIDS + 
                       log(GDP) + thinness..1.19.years +
                       Income.composition.of.resources + Schooling, data = training)

plot(sw.select.model)

Forward Selection Validation

fwd.train=regsubsets(Life.expectancy~infant.deaths + Alcohol + 
              percentage.expenditure + Measles + BMI + 
              under.five.deaths + Polio + Total.expenditure + 
              Diphtheria + HIV.AIDS + log(GDP) + 
              thinness..1.19.years + thinness.5.9.years +
              Income.composition.of.resources + Schooling,
                    data=training,method="forward",nvmax=15)

#Creating a prediction function 
predict.regsubsets =function (object , newdata ,id ,...){
  form=as.formula (object$call [[2]])
  mat=model.matrix(form ,newdata )
  coefi=coef(object ,id=id)
  xvars=names(coefi)
  mat[,xvars]%*%coefi
}

valMSE<-c()
#note my index, i, is to 15 since that is how many predictors I went up to during fwd selection
for (i in 1:15){
  predictions<-predict.regsubsets(object=fwd.train,newdata=validate,id=i) 
  valMSE[i]<-mean((validate$Life.expectancy-predictions)^2)
}
par(mfrow=c(1,1))
plot(1:15,sqrt(valMSE),type="l",xlab="# of predictors",
     ylab="test vs train RMSE")
index<-which(valMSE==min(valMSE))
points(index,sqrt(valMSE[index]),col="red",pch=10)

trainMSE<-summary(fwd.train)$rss/nrow(training)
lines(1:15,sqrt(trainMSE),lty=3,col="blue")  

Adding Complexity to the Model

# Transformations using Polio as a test

transformations <- training

# Transforming with Polynomial using a ^2
transformations$polio2 <- transformations$Polio^2
transformations %>% ggplot(aes(x=polio2, y=Life.expectancy)) +
geom_point() + geom_smooth()
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Transforming using Log
transformations$logPolio <- log(transformations$Polio)

transformations %>% ggplot(aes(x=logPolio, y=Life.expectancy)) +
geom_point() + geom_smooth()
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Testing if it's the same as logging inside the plot
transformations %>% ggplot(aes(x=log(Polio), y=Life.expectancy)) +
geom_point() + geom_smooth()
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Creating plot functions

# Original Data plot
plot_original <- function(var1) {
  return(training %>% ggplot(aes(x=var1, 
                                        y = Life.expectancy, 
                                        color=Status)) + 
           geom_point() + geom_smooth () + ylab("Life Expectancy in Age")
)
}

plot_original(training$Polio)+ 
  xlab("Polio Immunization Coverage among 1-year-olds")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Creating function to plot variable as polynomials 

plot_poly <- function(var1) {
  return(training %>% ggplot(aes(x=var1^2, 
                                      y = Life.expectancy,
                                      color=Status)) + 
         geom_point() + geom_smooth () + ylab("Life Expectancy in Age")
)
}

plot_poly(training$Polio)+ 
  xlab("Polio Immunization Coverage among 1-year-olds")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Creating function to plot variables as logged
plot_log <- function(var1) {
  return(training %>% ggplot(aes(x=log(var1), 
                                      y = Life.expectancy, 
                                      color=Status)) + 
         geom_point() + geom_smooth () + ylab("Life Expectancy in Age")
)
}

plot_log(training$Polio) + 
  xlab("Polio Immunization Coverage among 1-year-olds")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Putting each Variable into the Function

# Infant Deaths Variable

plot_original(training$infant.deaths) + xlab("Infant Deaths per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$infant.deaths) + xlab("Infant Deaths per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$infant.deaths) + xlab("Infant Deaths per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
## Warning: Removed 656 rows containing non-finite values (`stat_smooth()`).

# Alcohol Variable

plot_original(training$Alcohol) + 
  xlab("Alcohol Consumption per capita in Litres of pure alcohol")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$Alcohol) + 
  xlab("Alcohol Consumption per capita in Litres of pure alcohol")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$Alcohol) + 
  xlab("Alcohol Consumption per capita in Litres of pure alcohol")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Percentage of Expenditures Variable

plot_original(training$percentage.expenditure) + 
  xlab("Expenditure on health as a percentage of Gross Domestic Product per capita")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$percentage.expenditure) + 
  xlab("Expenditure on health as a percentage of Gross Domestic Product per capita")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$percentage.expenditure) + 
  xlab("Expenditure on health as a percentage of Gross Domestic Product per capita")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
## Warning: Removed 500 rows containing non-finite values (`stat_smooth()`).

# Measles Variable

plot_original(training$Measles) + xlab("Reported Measles cases per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$Measles)+ xlab("Reported Measles cases per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$Measles)+ xlab("Reported Measles cases per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
## Warning: Removed 778 rows containing non-finite values (`stat_smooth()`).

# BMI Variable

plot_original(training$BMI) + xlab("Average Body Mass Index of population")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$BMI)+ xlab("Average Body Mass Index of population")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$BMI)+ xlab("Average Body Mass Index of population")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Under Five Deaths Variable

plot_original(training$under.five.deaths) + 
  xlab("Under age 5 deaths per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$under.five.deaths)+ 
  xlab("Under age 5 deaths per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$under.five.deaths)+ 
  xlab("Under age 5 deaths per 1000")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
## Warning: Removed 604 rows containing non-finite values (`stat_smooth()`).

# Total Expenditures Variable

plot_original(training$Total.expenditure) + 
  xlab("Percentage of total government expenditures on health")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$Total.expenditure)+ 
  xlab("Percentage of total government expenditures on health")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$Total.expenditure)+ 
  xlab("Percentage of total government expenditures on health")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Diphtheria Variable

plot_original(training$Diphtheria) + 
  xlab("DPT3 Immunization Coverage among 1-year-olds")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$Diphtheria)+ 
  xlab("DPT3 Immunization Coverage among 1-year-olds")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$Diphtheria)+ 
  xlab("DPT3 Immunization Coverage among 1-year-olds")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# HIV AIDS Variable

plot_original(training$HIV.AIDS) + xlab ("HIV/AIDS Deaths per 1000 live births")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$HIV.AIDS)+ xlab ("HIV/AIDS Deaths per 1000 live births")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$HIV.AIDS)+ xlab ("HIV/AIDS Deaths per 1000 live births")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# GDP Variable

plot_original(training$GDP) + xlab("Gross Domestic Product per capita in USD")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$GDP)+ xlab("Gross Domestic Product per capita in USD")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$GDP)+ xlab("Gross Domestic Product per capita in USD")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Thinness 10-19 Years Variable

plot_original(training$thinness..1.19.years) + 
  xlab("Prevalence of thinness among children ages 10 to 19")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$thinness..1.19.years)+ 
  xlab("Prevalence of thinness among children ages 10 to 19")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$thinness..1.19.years)+ 
  xlab("Prevalence of thinness among children ages 10 to 19")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Thinness 5-9 Variable

plot_original(training$thinness.5.9.years)+ 
  xlab("Prevalence of thinness among children ages 5 to 9")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$thinness.5.9.years)+ 
  xlab("Prevalence of thinness among children ages 5 to 9")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$thinness.5.9.years)+ 
  xlab("Prevalence of thinness among children ages 5 to 9")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

# Income Composition of Resources Variable

plot_original(training$Income.composition.of.resources) + 
  xlab("Human Development Index in terms of income composition of resources")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$Income.composition.of.resources)+ 
  xlab("Human Development Index in terms of income composition of resources")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$Income.composition.of.resources)+ 
  xlab("Human Development Index in terms of income composition of resources")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
## Warning: Removed 101 rows containing non-finite values (`stat_smooth()`).

# Schooling Variable

plot_original(training$Schooling) + xlab("Years in School")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_poly(training$Schooling)+ xlab("Years in School")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

plot_log(training$Schooling)+ xlab("Years in School")
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
## Warning: Removed 21 rows containing non-finite values (`stat_smooth()`).

Original Model for comparison

original.model <- lm(Life.expectancy~ Polio + Alcohol + BMI +
                       Diphtheria+Schooling + HIV.AIDS + GDP +
                       thinness..1.19.years + Measles + Total.expenditure + 
                       Income.composition.of.resources, training)

plot(original.model)

Fitting a complex model with polynomials up to 2 & logged variables

poly2logmodel <- lm(Life.expectancy~ poly(Polio,2)+
                      poly(Alcohol,2)+
                      poly(BMI,2)+
                      poly(Diphtheria,2)+
                      poly(Schooling,2)+
                      log(HIV.AIDS) +
                      log(GDP) +
                      log(thinness..1.19.years) +
                      Measles +
                      Total.expenditure+
                      Income.composition.of.resources, training)

plot(poly2logmodel)

Fitting a complex model with polynomials up to 7 & logged variables

poly7logmodel <- lm(Life.expectancy~ poly(Polio,7)+
                      sqrt(Alcohol)+
                      poly(BMI,7)+
                      poly(Diphtheria,5)+
                      poly(Schooling,7)+
                      log(HIV.AIDS) +
                      log(GDP) +
                      log(thinness..1.19.years) +
                      Measles +
                      Total.expenditure+
                      Income.composition.of.resources, training)

plot(poly7logmodel)

Fitting interaction terms on regular model

interaction.model <- lm(Life.expectancy~ Polio:Status+Alcohol:Status+BMI:Status+
                          Diphtheria:Status+Schooling:Status+
                          HIV.AIDS:Status+GDP:Status+
                          thinness..1.19.years:Status+
                          Measles:Status+Total.expenditure:Status+
                          Income.composition.of.resources:Status, training)

plot(interaction.model)

Fitting interaction on poly2logmodel

poly2log.interaction.model <- lm(Life.expectancy~ poly(Polio,2):Status+
                      poly(Alcohol,2):Status+
                      poly(BMI,2):Status+
                      poly(Diphtheria,2):Status+
                      poly(Schooling,2):Status+
                      log(HIV.AIDS):Status +
                      log(GDP):Status +
                      log(thinness..1.19.years):Status +
                      Measles:Status +
                      Total.expenditure:Status+
                      Income.composition.of.resources:Status, training)

plot(poly2log.interaction.model)

Fitting interaction on poly7logmodel

poly7log.interaction.model <- lm(Life.expectancy~ poly(Polio,7):Status+
                      sqrt(Alcohol):Status+
                      poly(BMI,7):Status+
                      poly(Diphtheria,5):Status+
                      poly(Schooling,7):Status+
                      log(HIV.AIDS):Status +
                      log(GDP):Status +
                      log(thinness..1.19.years):Status +
                      Measles:Status +
                      Total.expenditure:Status+
                      Income.composition.of.resources:Status, training)

plot(poly7log.interaction.model)

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

Fitting a complex model with polynomials up to 7 & logged variables and categorical variable Status

status.poly7logmodel <- lm(Life.expectancy~ Status + poly(Polio,7)+
                      sqrt(Alcohol)+
                      poly(BMI,7)+
                      poly(Diphtheria,5)+
                      poly(Schooling,7)+
                      log(HIV.AIDS) +
                      log(GDP) +
                      log(thinness..1.19.years) +
                      Measles +
                      Total.expenditure+
                      Income.composition.of.resources, training)

plot(status.poly7logmodel)

Simple Model

simple <- lm(Life.expectancy ~ HIV.AIDS + Alcohol:Status + Total.expenditure, training)
plot(simple)

Predictions

# RMSE of Full Model
full.model_Preds = predict(full.model, newdata = validate)
as.data.frame(full.model_Preds)
##      full.model_Preds
## 1            61.26067
## 6            61.25329
## 7            60.65273
## 9            59.60362
## 10           58.92236
## 24           74.83362
## 28           74.02891
## 33           77.00425
## 35           75.13027
## 36           74.97686
## 42           72.21996
## 43           69.57465
## 48           69.55915
## 49           60.78034
## 57           57.42985
## 59           54.85236
## 60           50.96067
## 79           60.45561
## 80           60.34527
## 82           78.07716
## 105          69.87373
## 108          70.83053
## 115          85.80442
## 124          80.72788
## 129          80.11401
## 130          82.30248
## 136          79.67392
## 137          81.06677
## 151          70.70706
## 156          68.57278
## 157          69.05886
## 159          67.54161
## 164          73.31474
## 168          70.69792
## 174          75.33841
## 176          67.67137
## 182          73.59226
## 184          75.54608
## 186          75.27304
## 190          74.33864
## 193          67.93994
## 194          67.47006
## 201          64.58460
## 204          64.47756
## 206          63.11098
## 209          76.49412
## 210          78.66034
## 213          78.07706
## 218          74.81362
## 221          71.44372
## 223          73.59979
## 226          75.47800
## 232          74.12091
## 240          71.08439
## 242          81.74112
## 247          79.16743
## 258          70.34347
## 259          75.49176
## 264          70.95470
## 278          62.60389
## 285          59.68380
## 287          58.81592
## 288          58.80564
## 289          68.65665
## 296          63.03336
## 297          62.52069
## 298          61.92907
## 306          72.37380
## 307          71.99719
## 312          70.89394
## 318          69.60384
## 338          68.43750
## 339          65.99361
## 345          59.13624
## 351          41.36218
## 356          75.59812
## 368          74.39652
## 371          76.57313
## 375          75.42010
## 386          77.31309
## 402          60.53706
## 406          57.70129
## 409          57.33817
## 415          49.38363
## 418          63.46357
## 419          68.67638
## 426          56.78735
## 429          53.38613
## 430          52.96413
## 446          56.03499
## 448          58.46316
## 450          70.89334
## 451          74.03501
## 452          70.58919
## 453          65.60153
## 459          68.35909
## 460          71.43905
## 465          68.02868
## 468          65.67622
## 478          59.25434
## 480          56.73935
## 482          61.07593
## 492          54.28354
## 493          54.94886
## 503          78.47312
## 505          78.21713
## 509          76.75123
## 511          80.01854
## 513          54.66215
## 516          53.25230
## 518          51.22319
## 523          47.94482
## 527          53.17321
## 532          53.03313
## 537          50.44184
## 545          78.26372
## 555          76.23276
## 556          74.89891
## 559          76.87118
## 577          72.87396
## 580          73.72002
## 596          65.41644
## 601          62.04037
## 603          62.59913
## 614          62.23064
## 626          72.59401
## 627          74.94629
## 635          75.49435
## 642          78.56416
## 645          80.55068
## 646          80.48588
## 655          74.93939
## 658          74.89361
## 665          78.79516
## 673          72.64484
## 686          77.29558
## 698          77.40339
## 699          77.28158
## 701          72.96864
## 720          68.87919
## 729          64.11346
## 732          55.50850
## 751          82.77830
## 752          81.00838
## 758          60.54792
## 760          60.52456
## 767          55.46539
## 771          72.82218
## 774          72.08523
## 788          74.19228
## 798          69.16284
## 807          72.38294
## 816          70.71415
## 822          72.14057
## 823          69.55891
## 825          74.82460
## 835          63.61844
## 840          59.18490
## 847          59.03783
## 853          60.94309
## 858          58.84906
## 859          58.46482
## 864          51.12897
## 872          77.30293
## 876          75.83902
## 878          74.18127
## 881          72.85571
## 884          61.64156
## 894          47.99681
## 898          43.03886
## 899          74.33955
## 902          71.20336
## 904          77.07567
## 906          76.29953
## 911          75.04965
## 922          78.79857
## 925          81.58379
## 926          82.29014
## 931          78.97052
## 934          78.89706
## 935          76.28322
## 954          62.09361
## 958          58.40540
## 960          58.72495
## 961          65.45976
## 971          61.96682
## 978          62.89673
## 979          74.19063
## 988          72.61785
## 991          70.44544
## 994          64.09063
## 997          81.01196
## 1002         83.09800
## 1006         80.88864
## 1011         66.56119
## 1014         65.94491
## 1022         62.45891
## 1027         77.76387
## 1035         81.21623
## 1036         78.17917
## 1039         77.84228
## 1041         74.73272
## 1047         76.76778
## 1050         70.68826
## 1051         70.26622
## 1058         68.98664
## 1062         69.87859
## 1066         72.98096
## 1074         62.58279
## 1079         64.72901
## 1080         58.42432
## 1089         52.72789
## 1093         60.43136
## 1094         59.93821
## 1096         60.03466
## 1099         64.61338
## 1103         57.92276
## 1105         59.99954
## 1111         68.35948
## 1115         66.50798
## 1118         66.48528
## 1119         64.05795
## 1124         62.61022
## 1137         63.70072
## 1139         71.06561
## 1141         74.17934
## 1146         70.10478
## 1147         72.77551
## 1152         66.82886
## 1157         78.47627
## 1158         78.31439
## 1161         77.94188
## 1164         77.57724
## 1166         79.85573
## 1168         75.48242
## 1171         81.95540
## 1172         77.00966
## 1175         80.21250
## 1176         83.47097
## 1178         83.63715
## 1180         81.60848
## 1187         74.39915
## 1199         66.27350
## 1200         58.54447
## 1210         68.24230
## 1213         70.60980
## 1215         65.44742
## 1226         72.37365
## 1228         71.63007
## 1230         71.77070
## 1232         71.44366
## 1234         73.53859
## 1237         70.95676
## 1242         68.80128
## 1251         81.74908
## 1252         82.16723
## 1271         79.28824
## 1273         78.66971
## 1282         76.59033
## 1290         79.39172
## 1302         72.18958
## 1308         74.50858
## 1322         79.46708
## 1329         77.81666
## 1343         73.64361
## 1350         71.81748
## 1355         71.43616
## 1365         63.70149
## 1367         63.81420
## 1372         52.78211
## 1375         50.64488
## 1384         74.09210
## 1391         60.32075
## 1392         66.58653
## 1396         73.50889
## 1404         76.82749
## 1413         70.97077
## 1415         70.33928
## 1417         72.42024
## 1420         69.31712
## 1425         69.15294
## 1433         63.98719
## 1445         74.31894
## 1453         76.44117
## 1458         73.87289
## 1463         74.21620
## 1466         72.95992
## 1470         69.71167
## 1471         72.27778
## 1479         65.28012
## 1483         44.40123
## 1491         62.00417
## 1499         59.42746
## 1505         57.81228
## 1511         70.66425
## 1513         74.03039
## 1515         74.13309
## 1518         74.03156
## 1519         74.89908
## 1522         74.37450
## 1526         76.10020
## 1531         81.13934
## 1535         78.96978
## 1537         78.05632
## 1540         79.98241
## 1542         78.61888
## 1543         82.13737
## 1549         80.03595
## 1551         80.20399
## 1553         79.51121
## 1567         59.46084
## 1572         60.27111
## 1573         58.63110
## 1581         56.17871
## 1582         45.24143
## 1586         43.74642
## 1589         72.27284
## 1593         72.23559
## 1597         70.64191
## 1607         72.07051
## 1618         69.01550
## 1633         58.27802
## 1639         80.48554
## 1649         77.02704
## 1650         78.41154
## 1659         62.20869
## 1666         61.35165
## 1674         71.26340
## 1676         71.93883
## 1678         71.28925
## 1687         74.12743
## 1690         76.77096
## 1691         74.35092
## 1693         74.31292
## 1698         72.51517
## 1703         71.38522
## 1708         70.35378
## 1709         69.83454
## 1714         69.01766
## 1723         70.92811
## 1725         74.59687
## 1727         68.47520
## 1734         77.82207
## 1738         75.98911
## 1743         73.52955
## 1748         60.22807
## 1760         69.43011
## 1763         67.96592
## 1764         70.23886
## 1766         59.09903
## 1776         49.67722
## 1777         49.40628
## 1784         68.38165
## 1788         60.28282
## 1795         60.52830
## 1799         67.53719
## 1801         63.68714
## 1818         67.64458
## 1826         66.60507
## 1832         84.20504
## 1833         80.75648
## 1848         84.66074
## 1854         81.58015
## 1856         81.25280
## 1858         76.52578
## 1861         77.37639
## 1862         71.10876
## 1868         70.81789
## 1878         62.18695
## 1885         54.62909
## 1890         54.79334
## 1894         52.16337
## 1898         48.84572
## 1905         50.17582
## 1911         81.45713
## 1913         78.51893
## 1916         84.05204
## 1917         80.36208
## 1919         83.97371
## 1928         76.14337
## 1933         75.70497
## 1936         70.01843
## 1940         74.16504
## 1942         66.41219
## 1943         67.58376
## 1944         66.88284
## 1957         60.89326
## 1960         73.30585
## 1962         71.50394
## 1965         74.31239
## 1968         72.25169
## 1972         73.47151
## 1973         73.42822
## 1978         62.79254
## 1981         63.71125
## 1982         63.77439
## 1987         59.26406
## 1988         60.51353
## 1989         59.46951
## 1990         59.10188
## 1992         69.28675
## 1997         71.86502
## 2013         75.04512
## 2023         72.30816
## 2028         69.05994
## 2034         65.95696
## 2044         78.54676
## 2047         78.61202
## 2058         78.57927
## 2059         79.74113
## 2063         80.21992
## 2064         78.47558
## 2066         80.96229
## 2069         81.01337
## 2070         78.95487
## 2073         77.33613
## 2083         76.69285
## 2086         74.10816
## 2092         72.05113
## 2094         72.80439
## 2095         72.69141
## 2097         72.80530
## 2103         71.31606
## 2105         68.42389
## 2109         66.18064
## 2114         70.49592
## 2124         75.52770
## 2125         77.48903
## 2135         72.95187
## 2153         69.05643
## 2154         65.45010
## 2157         68.90564
## 2167         48.16775
## 2176         72.31260
## 2178         69.71304
## 2180         71.05502
## 2181         68.01170
## 2183         71.34602
## 2200         65.51069
## 2203         72.40223
## 2211         73.14440
## 2220         68.60466
## 2221         67.11558
## 2227         70.43672
## 2232         61.53878
## 2239         75.54473
## 2248         75.32969
## 2249         75.16571
## 2256         61.60326
## 2258         64.32687
## 2268         74.97930
## 2271         74.11240
## 2278         73.12376
## 2279         73.53800
## 2281         71.70544
## 2287         73.88375
## 2290         72.03015
## 2299         58.91737
## 2306         62.96140
## 2310         63.80234
## 2316         78.40795
## 2317         79.86662
## 2323         76.32631
## 2331         77.93472
## 2340         76.15935
## 2341         75.97860
## 2342         75.53683
## 2354         82.44785
## 2362         67.08579
## 2366         68.30863
## 2367         64.75274
## 2371         70.94259
## 2372         67.07289
## 2373         66.42331
## 2376         64.02547
## 2377         63.48928
## 2382         61.87313
## 2387         59.94652
## 2393         60.75624
## 2399         60.13116
## 2408         51.74584
## 2413         56.72200
## 2422         52.94270
## 2424         53.08168
## 2431         80.47557
## 2433         82.93065
## 2434         79.86608
## 2435         81.20473
## 2439         79.02208
## 2443         71.08408
## 2444         70.88130
## 2445         70.63995
## 2457         68.56457
## 2465         62.93749
## 2477         71.80044
## 2482         73.73269
## 2487         64.08091
## 2488         63.55243
## 2491         62.26392
## 2493         57.93611
## 2501         46.70820
## 2502         45.74855
## 2510         82.89974
## 2512         80.14572
## 2514         81.80502
## 2516         79.99246
## 2518         81.22974
## 2521         80.63873
## 2526         83.88032
## 2534         78.54076
## 2536         80.03437
## 2546         67.08964
## 2547         67.58613
## 2551         69.03516
## 2552         68.85413
## 2553         68.77617
## 2555         69.19757
## 2560         68.90774
## 2571         72.71689
## 2573         71.40022
## 2581         69.42250
## 2589         75.66872
## 2604         67.29214
## 2605         68.14342
## 2607         66.99834
## 2611         64.22273
## 2622         68.55977
## 2628         57.62845
## 2629         58.56526
## 2637         72.98061
## 2640         72.23984
## 2643         71.54781
## 2664         69.62246
## 2669         77.00904
## 2675         76.24912
## 2677         75.47013
## 2683         77.73642
## 2686         75.36037
## 2691         67.04733
## 2695         69.96050
## 2697         70.40811
## 2703         65.77438
## 2716         66.87861
## 2720         56.06326
## 2721         57.84550
## 2724         62.54252
## 2729         48.75268
## 2736         71.03306
## 2740         70.10523
## 2741         70.97990
## 2748         76.86509
## 2755         75.58542
## 2761         74.94314
## 2762         74.68309
## 2776         75.51017
## 2779         66.98068
## 2805         76.10658
## 2811         76.67608
## 2813         76.92180
## 2823         75.06191
## 2825         74.96602
## 2831         70.89561
## 2832         69.16266
## 2834         69.70554
## 2836         69.63792
## 2841         68.74777
## 2848         68.77698
## 2850         68.39281
## 2853         64.77474
## 2857         61.62546
## 2863         72.93319
## 2871         70.18832
## 2875         70.71543
## 2877         68.99531
## 2878         72.73195
## 2899         68.55200
## 2902         62.95071
## 2908         63.58455
## 2912         57.82892
## 2913         58.89341
## 2920         58.36194
## 2926         56.90191
## 2931         56.05016
## 2938         35.50959
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = full.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 4.041344
# RMSE of Preliminary Model
prelim.model_Preds = predict(prelim.model, newdata = validate)
as.data.frame(prelim.model_Preds)
##      prelim.model_Preds
## 1              62.04751
## 6              62.74015
## 7              62.01311
## 9              60.87087
## 10             60.04632
## 24             72.54378
## 28             72.12769
## 33             75.59255
## 35             75.69186
## 36             75.45854
## 42             72.35310
## 43             68.68529
## 48             69.30902
## 49             64.06578
## 57             61.61765
## 59             58.32458
## 60             54.00736
## 79             57.98654
## 80             57.73014
## 82             79.63243
## 105            69.82244
## 108            70.95617
## 115            84.69386
## 124            79.93350
## 129            79.47648
## 130            81.07708
## 136            77.44953
## 137            77.55651
## 151            70.62875
## 156            68.66137
## 157            69.26777
## 159            66.92714
## 164            75.16231
## 168            71.87967
## 174            73.77081
## 176            67.53821
## 182            73.01680
## 184            75.50084
## 186            75.26272
## 190            74.27318
## 193            65.75712
## 194            65.16881
## 201            63.64038
## 204            62.89307
## 206            60.16174
## 209            77.58922
## 210            77.77624
## 213            77.32595
## 218            75.73090
## 221            71.41896
## 223            74.37857
## 226            78.44514
## 232            77.37811
## 240            74.04369
## 242            80.34202
## 247            78.16179
## 258            71.53712
## 259            73.92091
## 264            72.23771
## 278            63.76620
## 285            60.82530
## 287            59.66091
## 288            59.56750
## 289            70.08372
## 296            62.84960
## 297            62.28214
## 298            61.67932
## 306            74.35705
## 307            73.92546
## 312            72.94290
## 318            71.95851
## 338            71.26691
## 339            68.21284
## 345            62.28553
## 351            43.13661
## 356            76.46245
## 368            74.70742
## 371            76.98761
## 375            75.74508
## 386            77.47407
## 402            61.89976
## 406            59.37030
## 409            59.53908
## 415            51.27583
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## 419            65.54297
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## 429            54.76492
## 430            54.31885
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## 904            75.54178
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## 911            73.41478
## 922            80.27118
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## 935            77.06686
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## 1014           68.15617
## 1022           57.71909
## 1027           78.09903
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## 1036           79.18271
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## 1051           70.22154
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## 1089           53.47888
## 1093           60.64473
## 1094           60.07679
## 1096           60.44908
## 1099           59.49710
## 1103           50.62736
## 1105           53.42487
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## 1115           67.79249
## 1118           67.56804
## 1119           64.60817
## 1124           63.15829
## 1137           58.58878
## 1139           71.66895
## 1141           72.19383
## 1146           70.75946
## 1147           70.36730
## 1152           66.61080
## 1157           79.16379
## 1158           79.13566
## 1161           78.87585
## 1164           78.64179
## 1166           77.39672
## 1168           76.02375
## 1171           81.13517
## 1172           73.85933
## 1175           78.52508
## 1176           82.46536
## 1178           82.56970
## 1180           80.94186
## 1187           65.45253
## 1199           58.48235
## 1200           58.11811
## 1210           67.13695
## 1213           65.80898
## 1215           63.27651
## 1226           72.74053
## 1228           71.80534
## 1230           71.98866
## 1232           71.72316
## 1234           71.11688
## 1237           68.01024
## 1242           68.94863
## 1251           81.29648
## 1252           81.70755
## 1271           79.82479
## 1273           79.61455
## 1282           77.04549
## 1290           77.98968
## 1302           72.72304
## 1308           72.47036
## 1322           77.76437
## 1329           76.13708
## 1343           74.55308
## 1350           74.38138
## 1355           75.50158
## 1365           64.96213
## 1367           65.76186
## 1372           54.26662
## 1375           52.58452
## 1384           72.12196
## 1391           59.00809
## 1392           67.15506
## 1396           73.21914
## 1404           77.34870
## 1413           72.35385
## 1415           71.67630
## 1417           70.06917
## 1420           71.58933
## 1425           70.92769
## 1433           64.43723
## 1445           74.06288
## 1453           78.32276
## 1458           75.00545
## 1463           74.46083
## 1466           72.92790
## 1470           65.82822
## 1471           69.11247
## 1479           60.78913
## 1483           46.65511
## 1491           62.63645
## 1499           59.19975
## 1505           58.88704
## 1511           71.44057
## 1513           74.89710
## 1515           75.05410
## 1518           75.13557
## 1519           76.38962
## 1522           75.77770
## 1526           76.62153
## 1531           79.04264
## 1535           76.19679
## 1537           74.98451
## 1540           76.80557
## 1542           75.66110
## 1543           79.56445
## 1549           77.58153
## 1551           78.67980
## 1553           78.20545
## 1567           60.96687
## 1572           63.68871
## 1573           61.26679
## 1581           48.30744
## 1582           48.86599
## 1586           46.27855
## 1589           72.78746
## 1593           72.87107
## 1597           70.90926
## 1607           70.96574
## 1618           68.87712
## 1633           54.54648
## 1639           79.26421
## 1649           75.50561
## 1650           75.40731
## 1659           62.00759
## 1666           61.39452
## 1674           72.48643
## 1676           73.13637
## 1678           72.47859
## 1687           74.33835
## 1690           74.94975
## 1691           74.94071
## 1693           74.64113
## 1698           72.13180
## 1703           73.03832
## 1708           71.89739
## 1709           71.24756
## 1714           70.19723
## 1723           73.75528
## 1725           72.89138
## 1727           71.55247
## 1734           77.10266
## 1738           77.21049
## 1743           74.67448
## 1748           57.52865
## 1760           69.13327
## 1763           67.39674
## 1764           66.78004
## 1766           61.88833
## 1776           50.53491
## 1777           50.36187
## 1784           64.64099
## 1788           62.93321
## 1795           60.10370
## 1799           69.19289
## 1801           64.52611
## 1818           67.49483
## 1826           62.38578
## 1832           83.13001
## 1833           80.23672
## 1848           83.83490
## 1854           81.19812
## 1856           80.83301
## 1858           74.60887
## 1861           75.97548
## 1862           71.43009
## 1868           71.65170
## 1878           58.84904
## 1885           56.67129
## 1890           52.32379
## 1894           61.38740
## 1898           59.59070
## 1905           55.66816
## 1911           80.82750
## 1913           77.19936
## 1916           82.23994
## 1917           79.58043
## 1919           82.18792
## 1928           74.61271
## 1933           74.27566
## 1936           69.46350
## 1940           72.19409
## 1942           64.59846
## 1943           63.47829
## 1944           62.45727
## 1957           56.77976
## 1960           74.07804
## 1962           71.54646
## 1965           75.37850
## 1968           72.59401
## 1972           74.47719
## 1973           74.42524
## 1978           64.23629
## 1981           65.68025
## 1982           65.68229
## 1987           60.88051
## 1988           62.48008
## 1989           61.50681
## 1990           60.94473
## 1992           69.34334
## 1997           72.89579
## 2013           72.97929
## 2023           73.24491
## 2028           69.99133
## 2034           66.17806
## 2044           78.74204
## 2047           75.52220
## 2058           77.45105
## 2059           79.06787
## 2063           79.65032
## 2064           77.76517
## 2066           78.67397
## 2069           78.84478
## 2070           76.13475
## 2073           77.23079
## 2083           76.94081
## 2086           74.04688
## 2092           70.97217
## 2094           71.97966
## 2095           71.80267
## 2097           72.03819
## 2103           71.30515
## 2105           68.24437
## 2109           67.59627
## 2114           73.60107
## 2124           74.66305
## 2125           77.80029
## 2135           72.51246
## 2153           65.55233
## 2154           66.73168
## 2157           65.40877
## 2167           49.22153
## 2176           73.28557
## 2178           70.06756
## 2180           72.03613
## 2181           68.21226
## 2183           72.68687
## 2200           64.62602
## 2203           73.10303
## 2211           70.83151
## 2220           69.89080
## 2221           67.71872
## 2227           67.39980
## 2232           60.69468
## 2239           75.89906
## 2248           73.70457
## 2249           73.31292
## 2256           61.34684
## 2258           60.56800
## 2268           75.64964
## 2271           74.73798
## 2278           74.01405
## 2279           74.54092
## 2281           72.06764
## 2287           71.52878
## 2290           73.74303
## 2299           64.36599
## 2306           58.34106
## 2310           60.36200
## 2316           76.81739
## 2317           78.06954
## 2323           74.21386
## 2331           77.61756
## 2340           75.98429
## 2341           75.67840
## 2342           75.19697
## 2354           80.40589
## 2362           67.35792
## 2366           69.10351
## 2367           64.66810
## 2371           67.67417
## 2372           63.22303
## 2373           62.49513
## 2376           64.71952
## 2377           63.99749
## 2382           66.15838
## 2387           63.81202
## 2393           65.25632
## 2399           64.12764
## 2408           51.83894
## 2413           58.36693
## 2422           54.59820
## 2424           54.94063
## 2431           79.68748
## 2433           80.56607
## 2434           78.89711
## 2435           80.17912
## 2439           77.98578
## 2443           71.20514
## 2444           70.97663
## 2445           70.72752
## 2457           69.13859
## 2465           64.88896
## 2477           73.36160
## 2482           71.78522
## 2487           63.80406
## 2488           63.11294
## 2491           65.86542
## 2493           60.51172
## 2501           32.39710
## 2502           29.02388
## 2510           81.28243
## 2512           79.28858
## 2514           80.49158
## 2516           79.18636
## 2518           80.29694
## 2521           79.79639
## 2526           81.28002
## 2534           76.99245
## 2536           78.21879
## 2546           65.45017
## 2547           66.40247
## 2551           68.60276
## 2552           68.24036
## 2553           68.25479
## 2555           69.27336
## 2560           69.41234
## 2571           73.70912
## 2573           72.11650
## 2581           70.21583
## 2589           74.28042
## 2604           66.53220
## 2605           67.85868
## 2607           66.54251
## 2611           63.46676
## 2622           65.11577
## 2628           59.28358
## 2629           60.39139
## 2637           73.71352
## 2640           72.72529
## 2643           72.33015
## 2664           71.02187
## 2669           75.74250
## 2675           74.73751
## 2677           73.83212
## 2683           76.77032
## 2686           75.93142
## 2691           65.63662
## 2695           69.48819
## 2697           70.44909
## 2703           65.55380
## 2716           63.57091
## 2720           58.22294
## 2721           60.89281
## 2724           58.67744
## 2729           55.20471
## 2736           73.22824
## 2740           73.62227
## 2741           74.72896
## 2748           76.98190
## 2755           75.57685
## 2761           73.16350
## 2762           72.91418
## 2776           73.57104
## 2779           70.17855
## 2805           75.13760
## 2811           78.28783
## 2813           78.67706
## 2823           76.13417
## 2825           76.12863
## 2831           72.04199
## 2832           69.79071
## 2834           70.23141
## 2836           70.31960
## 2841           69.19583
## 2848           68.65901
## 2850           68.31365
## 2853           63.30345
## 2857           59.60136
## 2863           74.10045
## 2871           71.01946
## 2875           70.38827
## 2877           68.29369
## 2878           70.00387
## 2899           64.92794
## 2902           63.88046
## 2908           66.16869
## 2912           60.06479
## 2913           61.21525
## 2920           52.28590
## 2926           60.07957
## 2931           47.80196
## 2938           34.98594
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = prelim.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 4.553895
# RMSE of Penalized Regression Model
glmnet.fit.model_Preds = predict(glmnet.fit.model, newdata = validate)
as.data.frame(glmnet.fit.model_Preds)
##      glmnet.fit.model_Preds
## 1                  62.35523
## 6                  62.67281
## 7                  62.02556
## 9                  60.95091
## 10                 60.20216
## 24                 72.46052
## 28                 71.86820
## 33                 75.36475
## 35                 75.44431
## 36                 75.24006
## 42                 72.24106
## 43                 69.25525
## 48                 69.36162
## 49                 63.51371
## 57                 60.24880
## 59                 57.17835
## 60                 53.34195
## 79                 58.53527
## 80                 58.55020
## 82                 79.32774
## 105                69.77798
## 108                70.83771
## 115                86.76511
## 124                79.39916
## 129                78.40820
## 130                82.34625
## 136                79.08912
## 137                78.97392
## 151                70.69320
## 156                68.76666
## 157                69.27415
## 159                67.29669
## 164                74.84179
## 168                71.57347
## 174                73.59167
## 176                68.16866
## 182                72.37954
## 184                74.95010
## 186                74.71285
## 190                73.78578
## 193                66.74138
## 194                66.05704
## 201                64.17292
## 204                63.72743
## 206                61.16809
## 209                76.72258
## 210                77.14006
## 213                76.69923
## 218                75.21708
## 221                71.42340
## 223                73.87786
## 226                78.31912
## 232                77.21102
## 240                74.02955
## 242                81.42737
## 247                77.80052
## 258                71.23730
## 259                73.65344
## 264                72.18938
## 278                63.52253
## 285                60.63556
## 287                59.58281
## 288                59.47714
## 289                69.57164
## 296                63.03386
## 297                62.49877
## 298                61.92074
## 306                74.04406
## 307                73.66647
## 312                72.76389
## 318                71.85276
## 338                70.80182
## 339                68.23858
## 345                62.18508
## 351                43.37143
## 356                77.07519
## 368                76.26226
## 371                76.56820
## 375                75.16696
## 386                77.11682
## 402                61.45941
## 406                58.61864
## 409                58.22848
## 415                50.17163
## 418                65.62581
## 419                65.39585
## 426                58.99348
## 429                55.19049
## 430                54.68733
## 446                60.55634
## 448                63.13903
## 450                70.13956
## 451                71.38975
## 452                69.91174
## 453                64.42812
## 459                67.50249
## 460                68.28602
## 465                68.32670
## 468                65.56309
## 478                59.85008
## 480                57.08189
## 482                64.11351
## 492                56.75949
## 493                57.51632
## 503                79.06163
## 505                79.66638
## 509                77.28953
## 511                79.52312
## 513                57.19517
## 516                56.29178
## 518                53.80144
## 523                50.85921
## 527                46.01421
## 532                54.68946
## 537                52.21660
## 545                78.56648
## 555                76.59486
## 556                75.00549
## 559                75.39371
## 577                73.58304
## 580                74.77862
## 596                66.54503
## 601                63.03211
## 603                63.91394
## 614                63.73996
## 626                71.92421
## 627                75.12179
## 635                73.81882
## 642                77.30661
## 645                78.10023
## 646                78.03784
## 655                73.81779
## 658                74.72450
## 665                77.30149
## 673                72.55794
## 686                75.23752
## 698                74.10335
## 699                74.01085
## 701                71.05498
## 720                69.45399
## 729                66.87479
## 732                60.07936
## 751                81.15581
## 752                78.52204
## 758                61.38802
## 760                61.51828
## 767                56.31448
## 771                73.67706
## 774                73.37554
## 788                74.78726
## 798                69.38276
## 807                73.41802
## 816                71.64256
## 822                73.62246
## 823                71.08553
## 825                72.96791
## 835                59.28977
## 840                60.98289
## 847                61.19458
## 853                61.67828
## 858                60.48095
## 859                60.16882
## 864                51.68358
## 872                79.11428
## 876                78.38648
## 878                76.56100
## 881                75.42758
## 884                62.45139
## 894                48.59831
## 898                43.40617
## 899                76.34398
## 902                72.49791
## 904                74.97766
## 906                74.60198
## 911                73.02822
## 922                79.79386
## 925                81.54304
## 926                82.35672
## 931                79.33635
## 934                79.81479
## 935                76.76854
## 954                63.03703
## 958                58.99015
## 960                59.31892
## 961                60.75581
## 971                63.21927
## 978                58.56985
## 979                74.78250
## 988                72.96700
## 991                70.53276
## 994                62.53010
## 997                80.17183
## 1002               81.50884
## 1006               80.45342
## 1011               68.31777
## 1014               67.66401
## 1022               57.90557
## 1027               77.78819
## 1035               80.94096
## 1036               78.64280
## 1039               78.49026
## 1041               74.87096
## 1047               75.08753
## 1050               70.96512
## 1051               70.45774
## 1058               69.46441
## 1062               71.03218
## 1066               70.58176
## 1074               63.08215
## 1079               60.46853
## 1080               59.21566
## 1089               53.90123
## 1093               61.05004
## 1094               60.48001
## 1096               60.62696
## 1099               59.87784
## 1103               52.14602
## 1105               54.68745
## 1111               70.23187
## 1115               67.68980
## 1118               67.87530
## 1119               65.15449
## 1124               63.79555
## 1137               59.30188
## 1139               71.37714
## 1141               72.01775
## 1146               70.58978
## 1147               70.25224
## 1152               66.57904
## 1157               78.44522
## 1158               78.43655
## 1161               78.49282
## 1164               78.44898
## 1166               77.20950
## 1168               75.95647
## 1171               80.28308
## 1172               75.67696
## 1175               78.46532
## 1176               83.02110
## 1178               83.51328
## 1180               80.41397
## 1187               76.86424
## 1199               67.93528
## 1200               59.34439
## 1210               69.11898
## 1213               67.85471
## 1215               65.55985
## 1226               72.53485
## 1228               71.71368
## 1230               71.86478
## 1232               71.68896
## 1234               71.09027
## 1237               68.32637
## 1242               69.24140
## 1251               80.41282
## 1252               81.23091
## 1271               79.79233
## 1273               78.71162
## 1282               76.50598
## 1290               77.74757
## 1302               72.55741
## 1308               72.09946
## 1322               78.77234
## 1329               76.93636
## 1343               74.13195
## 1350               73.82103
## 1355               75.31217
## 1365               64.66065
## 1367               65.27891
## 1372               54.05162
## 1375               51.91388
## 1384               71.98656
## 1391               60.17238
## 1392               67.63850
## 1396               72.76455
## 1404               77.01267
## 1413               71.88503
## 1415               71.47553
## 1417               69.78353
## 1420               71.38245
## 1425               70.65312
## 1433               64.53586
## 1445               73.76308
## 1453               77.75421
## 1458               74.68188
## 1463               74.08705
## 1466               72.70416
## 1470               66.17742
## 1471               69.47638
## 1479               60.66382
## 1483               47.07460
## 1491               63.15861
## 1499               60.17387
## 1505               59.56344
## 1511               71.02558
## 1513               74.43773
## 1515               74.52710
## 1518               74.69922
## 1519               75.80935
## 1522               75.23533
## 1526               76.53255
## 1531               78.91976
## 1535               76.11176
## 1537               74.94902
## 1540               80.13168
## 1542               75.51059
## 1543               83.16560
## 1549               77.35627
## 1551               80.55692
## 1553               79.54815
## 1567               61.31707
## 1572               63.41835
## 1573               61.29370
## 1581               48.40220
## 1582               48.56379
## 1586               45.87423
## 1589               72.21067
## 1593               72.20539
## 1597               70.25714
## 1607               70.49425
## 1618               68.41792
## 1633               53.35221
## 1639               79.36694
## 1649               75.19987
## 1650               75.11462
## 1659               62.04409
## 1666               61.54582
## 1674               71.87582
## 1676               72.62368
## 1678               72.01409
## 1687               74.62851
## 1690               75.19109
## 1691               74.98493
## 1693               74.92929
## 1698               72.67401
## 1703               72.76190
## 1708               71.64255
## 1709               71.07052
## 1714               70.11444
## 1723               73.40184
## 1725               72.65599
## 1727               71.36774
## 1734               76.48865
## 1738               76.77297
## 1743               74.26801
## 1748               58.13405
## 1760               69.24024
## 1763               67.69685
## 1764               67.08738
## 1766               62.01850
## 1776               50.61248
## 1777               50.60920
## 1784               64.69463
## 1788               61.66466
## 1795               60.53489
## 1799               68.90198
## 1801               64.95204
## 1818               67.45677
## 1826               62.71831
## 1832               82.41306
## 1833               79.38917
## 1848               85.46486
## 1854               80.78034
## 1856               80.41547
## 1858               75.21800
## 1861               76.35245
## 1862               71.45206
## 1868               71.54855
## 1878               57.80144
## 1885               54.61833
## 1890               49.90218
## 1894               54.23480
## 1898               51.62041
## 1905               45.10474
## 1911               79.98329
## 1913               76.57452
## 1916               85.13421
## 1917               79.06991
## 1919               84.97856
## 1928               74.01038
## 1933               73.70868
## 1936               69.00921
## 1940               71.67282
## 1942               64.99655
## 1943               67.13559
## 1944               66.15028
## 1957               59.76032
## 1960               73.57800
## 1962               71.94438
## 1965               75.06702
## 1968               72.46101
## 1972               73.91888
## 1973               73.85226
## 1978               64.77416
## 1981               65.82613
## 1982               65.91924
## 1987               61.25242
## 1988               62.98973
## 1989               62.19473
## 1990               61.59819
## 1992               69.18092
## 1997               72.73309
## 2013               73.00292
## 2023               73.03777
## 2028               70.32740
## 2034               66.66106
## 2044               78.20216
## 2047               75.54144
## 2058               77.30343
## 2059               78.70584
## 2063               79.89950
## 2064               77.50069
## 2066               78.74326
## 2069               78.75746
## 2070               75.97575
## 2073               77.49552
## 2083               77.00806
## 2086               73.53021
## 2092               70.78816
## 2094               71.85242
## 2095               71.70495
## 2097               71.89013
## 2103               71.53264
## 2105               68.77775
## 2109               67.77464
## 2114               73.41340
## 2124               74.88595
## 2125               77.53893
## 2135               72.44087
## 2153               65.67791
## 2154               66.45439
## 2157               65.48654
## 2167               49.81977
## 2176               73.10705
## 2178               70.04012
## 2180               71.95329
## 2181               68.66021
## 2183               72.52945
## 2200               64.96874
## 2203               72.97603
## 2211               70.99680
## 2220               69.50550
## 2221               67.68752
## 2227               67.33718
## 2232               61.48351
## 2239               75.42207
## 2248               73.25116
## 2249               72.90253
## 2256               61.72547
## 2258               60.34939
## 2268               75.54048
## 2271               74.68606
## 2278               73.81167
## 2279               74.26697
## 2281               72.17479
## 2287               71.49167
## 2290               73.39858
## 2299               64.55320
## 2306               58.52873
## 2310               60.32237
## 2316               76.12449
## 2317               78.49105
## 2323               73.89636
## 2331               77.21806
## 2340               75.67262
## 2341               75.35849
## 2342               74.91151
## 2354               80.45284
## 2362               67.18831
## 2366               68.98530
## 2367               65.08357
## 2371               67.66748
## 2372               63.81601
## 2373               63.13158
## 2376               64.92395
## 2377               64.37921
## 2382               65.20497
## 2387               62.78918
## 2393               64.26199
## 2399               64.10467
## 2408               51.66414
## 2413               58.63504
## 2422               54.77072
## 2424               54.96963
## 2431               79.19734
## 2433               81.25261
## 2434               78.61229
## 2435               80.65995
## 2439               77.78635
## 2443               70.88607
## 2444               70.67801
## 2445               70.36001
## 2457               68.86671
## 2465               64.32988
## 2477               73.21233
## 2482               71.60671
## 2487               64.43217
## 2488               63.80220
## 2491               65.59910
## 2493               60.37901
## 2501               33.22834
## 2502               30.55071
## 2510               83.20023
## 2512               78.71166
## 2514               81.43079
## 2516               78.57863
## 2518               80.60074
## 2521               79.77118
## 2526               85.22183
## 2534               76.80687
## 2536               79.26561
## 2546               66.09935
## 2547               66.73031
## 2551               68.56751
## 2552               68.34669
## 2553               68.26850
## 2555               69.46776
## 2560               69.35217
## 2571               73.39960
## 2573               71.85878
## 2581               70.20186
## 2589               73.77881
## 2604               66.67901
## 2605               67.67861
## 2607               66.44856
## 2611               63.67249
## 2622               65.04234
## 2628               59.61915
## 2629               60.59862
## 2637               73.62758
## 2640               72.96254
## 2643               71.97943
## 2664               70.57169
## 2669               75.27890
## 2675               74.22948
## 2677               73.36816
## 2683               76.21472
## 2686               75.82747
## 2691               66.47059
## 2695               70.02440
## 2697               70.78222
## 2703               66.06086
## 2716               63.23758
## 2720               58.11888
## 2721               60.31296
## 2724               57.87360
## 2729               53.98317
## 2736               73.37194
## 2740               73.98535
## 2741               74.56331
## 2748               77.00322
## 2755               75.65734
## 2761               72.71380
## 2762               72.47156
## 2776               73.63193
## 2779               69.49135
## 2805               75.21417
## 2811               77.46988
## 2813               77.99561
## 2823               75.71649
## 2825               75.71845
## 2831               72.02792
## 2832               69.79575
## 2834               70.59468
## 2836               70.50710
## 2841               69.41156
## 2848               68.72073
## 2850               68.38190
## 2853               63.98863
## 2857               60.68593
## 2863               74.11210
## 2871               71.13235
## 2875               70.12300
## 2877               68.27616
## 2878               69.77831
## 2899               65.01403
## 2902               64.01116
## 2908               65.76614
## 2912               60.08619
## 2913               60.70833
## 2920               52.10569
## 2926               59.95727
## 2931               48.05421
## 2938               35.32766
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = glmnet.fit.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 4.40931
# RMSE of Forward Selection Model
fwd.select.model_Preds = predict(fwd.select.model, newdata = validate)
as.data.frame(fwd.select.model_Preds)
##      fwd.select.model_Preds
## 1                  61.88016
## 6                  62.60091
## 7                  61.89848
## 9                  60.76923
## 10                 59.97893
## 24                 72.56463
## 28                 71.98484
## 33                 75.31887
## 35                 75.61679
## 36                 75.38591
## 42                 72.30002
## 43                 69.19530
## 48                 69.27844
## 49                 63.68341
## 57                 61.29284
## 59                 58.19025
## 60                 54.14158
## 79                 57.55694
## 80                 57.53642
## 82                 79.35914
## 105                69.57951
## 108                70.91714
## 115                86.78446
## 124                79.55472
## 129                78.92157
## 130                82.22867
## 136                78.65884
## 137                78.54446
## 151                70.69050
## 156                68.91862
## 157                69.31683
## 159                67.30154
## 164                74.82904
## 168                71.40163
## 174                73.38290
## 176                67.20493
## 182                72.82476
## 184                75.41957
## 186                75.18135
## 190                74.22578
## 193                65.74364
## 194                65.26057
## 201                63.64490
## 204                63.62985
## 206                61.12785
## 209                77.14885
## 210                77.20891
## 213                76.73632
## 218                75.13378
## 221                71.11053
## 223                73.84069
## 226                78.05946
## 232                76.83324
## 240                73.64515
## 242                81.30959
## 247                77.92540
## 258                71.22752
## 259                73.69424
## 264                72.14892
## 278                63.73794
## 285                60.79425
## 287                59.74216
## 288                59.63021
## 289                69.64273
## 296                62.67862
## 297                62.10863
## 298                61.50855
## 306                74.27013
## 307                73.82745
## 312                72.83939
## 318                71.87119
## 338                71.15127
## 339                68.54094
## 345                61.95413
## 351                42.84853
## 356                76.15974
## 368                74.45014
## 371                77.20010
## 375                75.75730
## 386                76.88260
## 402                62.23488
## 406                59.24736
## 409                59.44108
## 415                51.29065
## 418                65.91020
## 419                65.68693
## 426                58.80278
## 429                54.80272
## 430                54.34650
## 446                60.53126
## 448                63.27759
## 450                70.50163
## 451                71.75453
## 452                70.25017
## 453                63.47238
## 459                67.44349
## 460                68.22986
## 465                68.15029
## 468                65.44244
## 478                59.11366
## 480                56.47767
## 482                64.78808
## 492                57.33008
## 493                58.08250
## 503                79.21774
## 505                79.42498
## 509                77.32722
## 511                79.61155
## 513                56.34735
## 516                55.72949
## 518                53.01317
## 523                50.22395
## 527                44.75651
## 532                55.09191
## 537                52.75222
## 545                79.02309
## 555                76.62484
## 556                75.11743
## 559                75.60931
## 577                73.68855
## 580                74.79326
## 596                66.56119
## 601                62.80763
## 603                63.60854
## 614                63.43946
## 626                72.15267
## 627                75.43988
## 635                73.96361
## 642                77.74630
## 645                78.00045
## 646                77.88064
## 655                73.44997
## 658                75.06109
## 665                77.61174
## 673                72.73008
## 686                75.17491
## 698                73.71910
## 699                73.64411
## 701                70.61301
## 720                69.39762
## 729                67.20580
## 732                61.25051
## 751                81.15537
## 752                78.53554
## 758                61.33658
## 760                61.46220
## 767                55.63952
## 771                73.75689
## 774                73.24614
## 788                74.92661
## 798                69.08628
## 807                73.02387
## 816                71.42533
## 822                73.85088
## 823                70.99900
## 825                73.16031
## 835                58.32086
## 840                59.89312
## 847                60.21777
## 853                61.56791
## 858                60.39259
## 859                59.99018
## 864                50.46084
## 872                78.79341
## 876                77.97053
## 878                76.18373
## 881                76.03336
## 884                63.46374
## 894                51.53898
## 898                47.13165
## 899                76.73281
## 902                73.02216
## 904                75.39593
## 906                75.01985
## 911                73.35319
## 922                79.94773
## 925                81.62569
## 926                82.48747
## 931                79.95299
## 934                79.82623
## 935                76.75929
## 954                62.52203
## 958                58.06828
## 960                58.38729
## 961                59.80792
## 971                63.20694
## 978                57.82952
## 979                75.06879
## 988                72.96888
## 991                70.59748
## 994                61.35503
## 997                80.33341
## 1002               81.37077
## 1006               80.19104
## 1011               68.44194
## 1014               68.15830
## 1022               57.66059
## 1027               78.33005
## 1035               81.07641
## 1036               78.90055
## 1039               78.61717
## 1041               74.58960
## 1047               75.14450
## 1050               70.32755
## 1051               69.78815
## 1058               68.73643
## 1062               71.10530
## 1066               70.55332
## 1074               62.49948
## 1079               60.49803
## 1080               59.18959
## 1089               53.69153
## 1093               60.98860
## 1094               60.40551
## 1096               60.37824
## 1099               59.41872
## 1103               50.85330
## 1105               53.82217
## 1111               70.11103
## 1115               67.44727
## 1118               67.55041
## 1119               64.21185
## 1124               63.47160
## 1137               58.47265
## 1139               71.51896
## 1141               72.12518
## 1146               70.68714
## 1147               70.30886
## 1152               66.51149
## 1157               78.56629
## 1158               78.53163
## 1161               78.53730
## 1164               78.25429
## 1166               77.00731
## 1168               75.69230
## 1171               80.87708
## 1172               74.92594
## 1175               78.74349
## 1176               83.25011
## 1178               83.70840
## 1180               80.79164
## 1187               66.59494
## 1199               60.06302
## 1200               59.70317
## 1210               67.66818
## 1213               66.41231
## 1215               63.91748
## 1226               72.67349
## 1228               71.74228
## 1230               71.92551
## 1232               71.77034
## 1234               71.19657
## 1237               67.85281
## 1242               68.87571
## 1251               81.03828
## 1252               81.39460
## 1271               80.29530
## 1273               79.30164
## 1282               76.99430
## 1290               77.94207
## 1302               72.78431
## 1308               72.29235
## 1322               78.96428
## 1329               76.99320
## 1343               74.54829
## 1350               73.86929
## 1355               75.19901
## 1365               64.87089
## 1367               65.76574
## 1372               54.19697
## 1375               52.66970
## 1384               72.26503
## 1391               59.22920
## 1392               67.36884
## 1396               73.31539
## 1404               77.57732
## 1413               72.33063
## 1415               71.53965
## 1417               69.88160
## 1420               71.46407
## 1425               70.81718
## 1433               64.05246
## 1445               73.66043
## 1453               77.80961
## 1458               74.74331
## 1463               74.34013
## 1466               72.93705
## 1470               65.66261
## 1471               69.02619
## 1479               60.64156
## 1483               46.61099
## 1491               62.53663
## 1499               59.53515
## 1505               58.81018
## 1511               71.47628
## 1513               74.94923
## 1515               75.12396
## 1518               75.31019
## 1519               76.30378
## 1522               75.67772
## 1526               76.14265
## 1531               78.69990
## 1535               75.96337
## 1537               74.84400
## 1540               79.79128
## 1542               75.43615
## 1543               82.83351
## 1549               77.29434
## 1551               80.26098
## 1553               79.26580
## 1567               61.71554
## 1572               63.80161
## 1573               61.46944
## 1581               48.81182
## 1582               49.08820
## 1586               46.54382
## 1589               72.68475
## 1593               72.65373
## 1597               70.64401
## 1607               70.72256
## 1618               68.57363
## 1633               55.06273
## 1639               79.59222
## 1649               75.43632
## 1650               75.33656
## 1659               61.91777
## 1666               61.55276
## 1674               72.18636
## 1676               72.87609
## 1678               72.19488
## 1687               74.31805
## 1690               74.82942
## 1691               74.60897
## 1693               74.54491
## 1698               72.14227
## 1703               72.92576
## 1708               71.82940
## 1709               71.15933
## 1714               70.10225
## 1723               73.63585
## 1725               72.80158
## 1727               71.55623
## 1734               77.10587
## 1738               76.96596
## 1743               74.55549
## 1748               57.64071
## 1760               69.15791
## 1763               67.42422
## 1764               66.85964
## 1766               62.02374
## 1776               50.87072
## 1777               50.93050
## 1784               64.53099
## 1788               62.90688
## 1795               60.28005
## 1799               69.07827
## 1801               64.52680
## 1818               67.38104
## 1826               62.46970
## 1832               82.75603
## 1833               79.64282
## 1848               85.57769
## 1854               80.96418
## 1856               80.58801
## 1858               74.66297
## 1861               75.81871
## 1862               71.56826
## 1868               71.64512
## 1878               58.85450
## 1885               56.72476
## 1890               52.98176
## 1894               61.60271
## 1898               59.78480
## 1905               56.12052
## 1911               80.45689
## 1913               76.97365
## 1916               85.26710
## 1917               79.48120
## 1919               85.11358
## 1928               74.53978
## 1933               74.15574
## 1936               69.34731
## 1940               72.04356
## 1942               64.71473
## 1943               63.28890
## 1944               62.46637
## 1957               57.19649
## 1960               73.64775
## 1962               71.32228
## 1965               75.21317
## 1968               72.50694
## 1972               74.16542
## 1973               74.11736
## 1978               64.50335
## 1981               65.69236
## 1982               65.72388
## 1987               60.92420
## 1988               62.64524
## 1989               61.81834
## 1990               61.08612
## 1992               69.31911
## 1997               72.66652
## 2013               73.02938
## 2023               73.18288
## 2028               69.91458
## 2034               66.06496
## 2044               78.15492
## 2047               75.47033
## 2058               77.34027
## 2059               78.69104
## 2063               79.77002
## 2064               77.37496
## 2066               78.57620
## 2069               78.63052
## 2070               75.77235
## 2073               77.91669
## 2083               77.47921
## 2086               73.99287
## 2092               70.56463
## 2094               71.62948
## 2095               71.44192
## 2097               71.70504
## 2103               71.29068
## 2105               67.80231
## 2109               67.02805
## 2114               73.18275
## 2124               74.78229
## 2125               77.51814
## 2135               72.19091
## 2153               65.84937
## 2154               66.73110
## 2157               65.19512
## 2167               49.06266
## 2176               72.79351
## 2178               69.44111
## 2180               71.54476
## 2181               67.57994
## 2183               72.20464
## 2200               64.45209
## 2203               73.18058
## 2211               70.72998
## 2220               69.83876
## 2221               67.95340
## 2227               67.19343
## 2232               60.85635
## 2239               75.84006
## 2248               73.61203
## 2249               73.22592
## 2256               62.00051
## 2258               60.75805
## 2268               75.42939
## 2271               74.47489
## 2278               73.75898
## 2279               74.31473
## 2281               72.20673
## 2287               71.53650
## 2290               73.34959
## 2299               64.63164
## 2306               58.26886
## 2310               60.27569
## 2316               76.74036
## 2317               79.00761
## 2323               74.33534
## 2331               77.24908
## 2340               75.61101
## 2341               75.33396
## 2342               74.86726
## 2354               80.46990
## 2362               67.16850
## 2366               69.17440
## 2367               64.57168
## 2371               67.80468
## 2372               63.55399
## 2373               62.49774
## 2376               64.84428
## 2377               64.30323
## 2382               66.18064
## 2387               63.55954
## 2393               65.07776
## 2399               64.00996
## 2408               51.39364
## 2413               58.32911
## 2422               54.52531
## 2424               54.86785
## 2431               79.40929
## 2433               81.21631
## 2434               78.57848
## 2435               80.52530
## 2439               77.64752
## 2443               71.10625
## 2444               70.87978
## 2445               70.60551
## 2457               69.11885
## 2465               64.90452
## 2477               73.19001
## 2482               71.59412
## 2487               63.69394
## 2488               63.01528
## 2491               65.87162
## 2493               60.49148
## 2501               32.20767
## 2502               29.45742
## 2510               83.36750
## 2512               79.05783
## 2514               81.66751
## 2516               78.97223
## 2518               80.89302
## 2521               80.11334
## 2526               85.05551
## 2534               76.73668
## 2536               79.07360
## 2546               65.51354
## 2547               66.22872
## 2551               68.55059
## 2552               68.17821
## 2553               68.19443
## 2555               69.61042
## 2560               69.50348
## 2571               73.41186
## 2573               71.81726
## 2581               69.93038
## 2589               74.24682
## 2604               66.70458
## 2605               67.73614
## 2607               66.43263
## 2611               63.42605
## 2622               65.13076
## 2628               59.30153
## 2629               60.42056
## 2637               73.98137
## 2640               73.28488
## 2643               72.27642
## 2664               70.70485
## 2669               75.67404
## 2675               74.66027
## 2677               73.75040
## 2683               76.51511
## 2686               75.94979
## 2691               65.54691
## 2695               69.71027
## 2697               70.54401
## 2703               65.53402
## 2716               63.63255
## 2720               57.88117
## 2721               60.67762
## 2724               58.55200
## 2729               55.61200
## 2736               72.88166
## 2740               74.12112
## 2741               74.56128
## 2748               77.43010
## 2755               75.99202
## 2761               73.05869
## 2762               72.80454
## 2776               73.19628
## 2779               70.01113
## 2805               74.83855
## 2811               77.90332
## 2813               78.29970
## 2823               75.91073
## 2825               75.83854
## 2831               71.99738
## 2832               69.68901
## 2834               70.45115
## 2836               70.40491
## 2841               69.33142
## 2848               68.64866
## 2850               68.28396
## 2853               63.39802
## 2857               59.60178
## 2863               73.87062
## 2871               70.78825
## 2875               70.01921
## 2877               67.85244
## 2878               69.60898
## 2899               64.72463
## 2902               63.80668
## 2908               66.14400
## 2912               60.08483
## 2913               61.15184
## 2920               52.66012
## 2926               59.87781
## 2931               47.84722
## 2938               35.07525
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = fwd.select.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 4.528587
# RMSE of Backward Selection Model
bck.select.model_Preds = predict(bck.select.model, newdata = validate)
as.data.frame(bck.select.model_Preds)
##      bck.select.model_Preds
## 1                  62.35462
## 6                  62.67258
## 7                  62.02852
## 9                  60.94398
## 10                 60.19891
## 24                 72.45860
## 28                 71.86594
## 33                 75.36348
## 35                 75.44416
## 36                 75.23874
## 42                 72.24103
## 43                 69.26258
## 48                 69.35749
## 49                 63.49404
## 57                 60.22242
## 59                 57.14034
## 60                 53.30397
## 79                 58.52821
## 80                 58.54316
## 82                 79.32152
## 105                69.77544
## 108                70.84197
## 115                86.76667
## 124                79.38567
## 129                78.40651
## 130                82.34958
## 136                79.08498
## 137                78.96737
## 151                70.69176
## 156                68.76962
## 157                69.27981
## 159                67.29576
## 164                74.84303
## 168                71.56387
## 174                73.58987
## 176                68.15669
## 182                72.37043
## 184                74.95051
## 186                74.71370
## 190                73.78694
## 193                66.73356
## 194                66.04637
## 201                64.15960
## 204                63.71935
## 206                61.13064
## 209                76.72039
## 210                77.13825
## 213                76.69602
## 218                75.21236
## 221                71.42197
## 223                73.87327
## 226                78.31535
## 232                77.20625
## 240                74.02606
## 242                81.42170
## 247                77.79355
## 258                71.22625
## 259                73.65063
## 264                72.18683
## 278                63.51290
## 285                60.62594
## 287                59.59634
## 288                59.48417
## 289                69.57409
## 296                63.03187
## 297                62.49652
## 298                61.91832
## 306                74.03872
## 307                73.66055
## 312                72.75561
## 318                71.84437
## 338                70.80034
## 339                68.23957
## 345                62.18305
## 351                43.36736
## 356                77.06810
## 368                76.24421
## 371                76.56451
## 375                75.16300
## 386                77.11614
## 402                61.44637
## 406                58.61371
## 409                58.21016
## 415                50.16276
## 418                65.61681
## 419                65.38744
## 426                58.99119
## 429                55.18062
## 430                54.68029
## 446                60.55741
## 448                63.14302
## 450                70.13034
## 451                71.38501
## 452                69.90851
## 453                64.42315
## 459                67.49976
## 460                68.28299
## 465                68.31591
## 468                65.56184
## 478                59.85027
## 480                57.12582
## 482                64.09909
## 492                56.74010
## 493                57.49828
## 503                79.06376
## 505                79.67062
## 509                77.27992
## 511                79.52262
## 513                57.18926
## 516                56.28456
## 518                53.79045
## 523                50.85396
## 527                46.01103
## 532                54.66775
## 537                52.19121
## 545                78.56341
## 555                76.59165
## 556                75.00360
## 559                75.39030
## 577                73.58023
## 580                74.77557
## 596                66.54164
## 601                63.02448
## 603                63.91157
## 614                63.73233
## 626                71.91282
## 627                75.12351
## 635                73.81789
## 642                77.30548
## 645                78.09916
## 646                78.03660
## 655                73.81563
## 658                74.72538
## 665                77.29492
## 673                72.55671
## 686                75.23513
## 698                74.10135
## 699                74.00901
## 701                71.04313
## 720                69.44588
## 729                66.86392
## 732                60.74240
## 751                81.15443
## 752                78.51994
## 758                61.39023
## 760                61.51932
## 767                56.31361
## 771                73.67512
## 774                73.37162
## 788                74.78516
## 798                69.38020
## 807                73.41003
## 816                71.63466
## 822                73.61984
## 823                71.08459
## 825                72.96525
## 835                59.29213
## 840                60.97696
## 847                61.18111
## 853                61.67355
## 858                60.47669
## 859                60.16422
## 864                51.67610
## 872                79.10985
## 876                78.38016
## 878                76.55609
## 881                75.42474
## 884                62.45854
## 894                48.53334
## 898                43.33252
## 899                76.34330
## 902                72.48620
## 904                74.97549
## 906                74.59919
## 911                73.02648
## 922                79.79177
## 925                81.54114
## 926                82.35379
## 931                79.33333
## 934                79.81572
## 935                76.81801
## 954                63.03154
## 958                58.97893
## 960                59.31397
## 961                60.76936
## 971                63.21510
## 978                58.55634
## 979                74.78260
## 988                72.96758
## 991                70.53338
## 994                62.51864
## 997                80.17978
## 1002               81.50607
## 1006               80.44638
## 1011               68.30543
## 1014               67.65703
## 1022               57.89032
## 1027               77.78751
## 1035               80.94064
## 1036               78.64197
## 1039               78.48846
## 1041               74.87124
## 1047               75.08367
## 1050               70.95014
## 1051               70.44264
## 1058               69.45061
## 1062               71.02765
## 1066               70.57669
## 1074               63.06950
## 1079               60.45670
## 1080               59.20053
## 1089               53.90791
## 1093               61.04750
## 1094               60.47736
## 1096               60.62311
## 1099               59.87380
## 1103               52.14165
## 1105               54.67268
## 1111               70.23085
## 1115               67.68121
## 1118               67.87354
## 1119               65.14964
## 1124               63.79384
## 1137               59.29419
## 1139               71.37365
## 1141               72.01712
## 1146               70.58759
## 1147               70.24956
## 1152               66.56889
## 1157               78.44316
## 1158               78.43451
## 1161               78.49067
## 1164               78.44705
## 1166               77.20849
## 1168               75.95470
## 1171               80.27936
## 1172               75.66609
## 1175               78.46511
## 1176               83.01998
## 1178               83.51246
## 1180               80.41211
## 1187               77.09365
## 1199               67.82032
## 1200               59.16509
## 1210               69.14667
## 1213               67.88119
## 1215               65.61874
## 1226               72.53585
## 1228               71.71418
## 1230               71.86323
## 1232               71.72372
## 1234               71.13230
## 1237               68.32758
## 1242               69.25836
## 1251               80.40907
## 1252               81.22775
## 1271               79.79316
## 1273               78.71110
## 1282               76.50538
## 1290               77.75363
## 1302               72.55530
## 1308               72.09430
## 1322               78.81115
## 1329               77.01857
## 1343               74.13519
## 1350               73.80640
## 1355               75.30400
## 1365               64.64110
## 1367               65.27001
## 1372               54.03404
## 1375               51.89006
## 1384               71.98264
## 1391               60.15507
## 1392               67.63273
## 1396               72.75361
## 1404               77.01100
## 1413               71.88217
## 1415               71.47249
## 1417               69.77309
## 1420               71.37821
## 1425               70.64685
## 1433               64.52877
## 1445               73.75042
## 1453               77.75068
## 1458               74.67943
## 1463               74.09041
## 1466               72.70940
## 1470               66.16192
## 1471               69.47210
## 1479               60.66008
## 1483               47.07432
## 1491               63.15628
## 1499               60.16438
## 1505               59.55807
## 1511               71.01771
## 1513               74.43878
## 1515               74.52561
## 1518               74.70841
## 1519               75.80776
## 1522               75.23247
## 1526               76.51939
## 1531               78.91634
## 1535               76.10998
## 1537               74.94781
## 1540               80.12474
## 1542               75.49953
## 1543               83.16913
## 1549               77.35543
## 1551               80.55740
## 1553               79.54749
## 1567               61.54786
## 1572               63.41153
## 1573               61.27849
## 1581               48.39021
## 1582               48.55295
## 1586               45.85587
## 1589               72.21078
## 1593               72.20417
## 1597               70.25472
## 1607               70.49857
## 1618               68.42102
## 1633               53.34012
## 1639               79.36923
## 1649               75.19958
## 1650               75.11395
## 1659               62.04003
## 1666               61.54115
## 1674               71.86737
## 1676               72.61960
## 1678               72.01020
## 1687               74.62398
## 1690               75.18524
## 1691               74.97859
## 1693               74.92191
## 1698               72.66445
## 1703               72.76650
## 1708               71.64646
## 1709               71.07390
## 1714               70.11499
## 1723               73.39636
## 1725               72.65103
## 1727               71.36375
## 1734               76.48813
## 1738               76.77129
## 1743               74.26893
## 1748               58.13335
## 1760               69.26311
## 1763               67.70459
## 1764               67.11271
## 1766               61.99958
## 1776               50.62335
## 1777               50.69692
## 1784               64.69357
## 1788               61.64659
## 1795               60.52777
## 1799               68.90841
## 1801               64.95535
## 1818               67.46596
## 1826               62.76775
## 1832               82.42364
## 1833               79.37875
## 1848               85.46744
## 1854               80.77766
## 1856               80.41263
## 1858               75.20294
## 1861               76.34713
## 1862               71.45021
## 1868               71.54606
## 1878               57.81264
## 1885               54.60249
## 1890               50.08938
## 1894               54.14869
## 1898               51.54606
## 1905               45.05831
## 1911               79.98016
## 1913               76.56510
## 1916               85.13770
## 1917               79.07035
## 1919               84.98089
## 1928               74.01153
## 1933               73.70879
## 1936               69.00111
## 1940               71.67275
## 1942               64.98905
## 1943               67.08865
## 1944               66.10422
## 1957               59.71682
## 1960               73.57598
## 1962               71.94275
## 1965               75.06636
## 1968               72.45881
## 1972               73.91649
## 1973               73.85048
## 1978               64.76960
## 1981               65.81772
## 1982               65.91139
## 1987               61.24678
## 1988               62.99977
## 1989               62.25980
## 1990               61.60859
## 1992               69.16985
## 1997               72.73130
## 2013               72.99776
## 2023               73.02816
## 2028               70.33314
## 2034               66.63676
## 2044               78.19915
## 2047               75.54013
## 2058               77.29215
## 2059               78.70457
## 2063               79.89780
## 2064               77.49870
## 2066               78.74053
## 2069               78.75379
## 2070               75.96335
## 2073               77.49748
## 2083               77.01004
## 2086               73.53124
## 2092               70.77571
## 2094               71.84462
## 2095               71.69656
## 2097               71.88142
## 2103               71.65026
## 2105               68.76832
## 2109               67.76649
## 2114               73.41241
## 2124               74.90091
## 2125               77.53650
## 2135               72.43771
## 2153               65.66924
## 2154               66.44439
## 2157               65.47851
## 2167               49.80968
## 2176               73.10450
## 2178               70.02914
## 2180               71.94906
## 2181               68.65326
## 2183               72.52473
## 2200               64.94800
## 2203               72.97717
## 2211               70.99393
## 2220               69.50532
## 2221               67.68754
## 2227               67.33467
## 2232               61.47882
## 2239               75.42535
## 2248               73.25317
## 2249               72.90363
## 2256               61.71697
## 2258               60.33987
## 2268               75.53368
## 2271               74.67985
## 2278               73.81092
## 2279               74.26704
## 2281               72.17354
## 2287               71.48768
## 2290               73.39197
## 2299               64.55485
## 2306               58.50975
## 2310               60.31839
## 2316               76.11899
## 2317               78.48562
## 2323               73.88390
## 2331               77.21717
## 2340               75.66992
## 2341               75.35572
## 2342               74.90766
## 2354               80.45045
## 2362               67.17573
## 2366               68.98131
## 2367               65.07847
## 2371               67.66409
## 2372               63.81601
## 2373               63.12474
## 2376               64.92034
## 2377               64.37443
## 2382               65.25402
## 2387               62.76636
## 2393               64.25975
## 2399               64.14544
## 2408               51.65729
## 2413               58.63147
## 2422               54.75859
## 2424               54.95667
## 2431               79.19795
## 2433               81.25336
## 2434               78.61159
## 2435               80.65963
## 2439               77.78329
## 2443               70.89464
## 2444               70.68833
## 2445               70.36139
## 2457               68.93174
## 2465               64.31445
## 2477               73.21199
## 2482               71.60543
## 2487               64.42332
## 2488               63.79459
## 2491               65.59690
## 2493               60.37180
## 2501               33.22684
## 2502               30.55331
## 2510               83.20544
## 2512               78.71251
## 2514               81.43195
## 2516               78.57886
## 2518               80.60097
## 2521               79.77009
## 2526               85.23042
## 2534               76.80133
## 2536               79.26072
## 2546               66.09816
## 2547               66.72814
## 2551               68.56835
## 2552               68.34675
## 2553               68.26763
## 2555               69.46605
## 2560               69.34749
## 2571               73.39456
## 2573               71.86868
## 2581               70.21185
## 2589               73.77922
## 2604               66.67454
## 2605               67.67294
## 2607               66.44248
## 2611               63.66643
## 2622               65.03378
## 2628               59.61284
## 2629               60.59139
## 2637               73.62663
## 2640               72.96219
## 2643               71.96553
## 2664               70.56827
## 2669               75.28162
## 2675               74.22921
## 2677               73.36785
## 2683               76.21580
## 2686               75.82648
## 2691               66.46803
## 2695               70.05103
## 2697               70.83960
## 2703               66.04604
## 2716               63.21850
## 2720               58.09803
## 2721               60.29192
## 2724               57.86558
## 2729               54.13226
## 2736               73.36943
## 2740               74.15144
## 2741               74.56966
## 2748               77.00620
## 2755               75.65670
## 2761               72.71364
## 2762               72.47140
## 2776               73.63033
## 2779               69.46871
## 2805               75.21605
## 2811               77.46735
## 2813               77.99503
## 2823               75.71359
## 2825               75.71624
## 2831               72.02366
## 2832               69.78290
## 2834               70.58914
## 2836               70.50319
## 2841               69.40338
## 2848               68.71620
## 2850               68.37612
## 2853               63.97558
## 2857               60.67069
## 2863               74.10814
## 2871               71.12730
## 2875               70.12039
## 2877               68.27702
## 2878               69.77766
## 2899               65.01108
## 2902               64.05649
## 2908               65.75373
## 2912               60.13204
## 2913               60.69048
## 2920               52.18878
## 2926               59.94256
## 2931               48.04391
## 2938               35.32895
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = bck.select.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 4.412429
# RMSE of Backward Selection Model
sw.select.model_Preds = predict(sw.select.model, newdata = validate)
as.data.frame(sw.select.model_Preds)
##      sw.select.model_Preds
## 1                 61.31254
## 6                 61.86068
## 7                 61.12008
## 9                 60.37020
## 10                59.47158
## 24                72.64839
## 28                71.93454
## 33                75.36283
## 35                75.46759
## 36                75.37724
## 42                72.65004
## 43                69.64285
## 48                69.57267
## 49                63.57112
## 57                61.47412
## 59                58.33431
## 60                54.19348
## 79                57.62813
## 80                57.67492
## 82                79.64893
## 105               69.80748
## 108               70.99819
## 115               86.68206
## 124               79.25224
## 129               78.96166
## 130               81.68167
## 136               79.47028
## 137               79.37008
## 151               70.71504
## 156               68.65508
## 157               69.20891
## 159               67.53956
## 164               74.66161
## 168               71.12654
## 174               73.50082
## 176               67.47864
## 182               73.06985
## 184               75.84213
## 186               75.50895
## 190               74.53136
## 193               65.57621
## 194               65.50276
## 201               63.82117
## 204               64.10597
## 206               61.62822
## 209               77.19218
## 210               77.00608
## 213               76.64391
## 218               75.21456
## 221               71.14486
## 223               73.87927
## 226               78.20041
## 232               76.91327
## 240               73.68579
## 242               82.16249
## 247               78.69179
## 258               71.17502
## 259               73.73655
## 264               72.20087
## 278               63.78275
## 285               60.84011
## 287               59.76637
## 288               59.70083
## 289               69.49776
## 296               62.46875
## 297               61.98637
## 298               61.46454
## 306               74.30248
## 307               73.90796
## 312               73.05325
## 318               71.84380
## 338               71.17880
## 339               68.58751
## 345               62.11091
## 351               42.90841
## 356               75.86537
## 368               74.28786
## 371               77.66841
## 375               76.15484
## 386               76.58310
## 402               62.30147
## 406               58.90805
## 409               59.16151
## 415               51.27319
## 418               65.64221
## 419               65.31184
## 426               57.90332
## 429               54.78204
## 430               54.33070
## 446               60.60161
## 448               63.16665
## 450               70.57689
## 451               71.94907
## 452               70.43284
## 453               63.54469
## 459               67.54436
## 460               68.17785
## 465               68.15177
## 468               65.30189
## 478               58.91482
## 480               56.37811
## 482               65.01257
## 492               57.46386
## 493               58.13201
## 503               78.56883
## 505               79.08159
## 509               76.84823
## 511               79.28606
## 513               56.23883
## 516               55.91381
## 518               53.11466
## 523               50.32862
## 527               44.96523
## 532               55.28718
## 537               53.06476
## 545               79.13603
## 555               76.59488
## 556               75.08291
## 559               75.59831
## 577               73.80322
## 580               74.71029
## 596               66.33006
## 601               62.86577
## 603               63.73402
## 614               63.85939
## 626               72.15457
## 627               75.03440
## 635               73.72764
## 642               77.83605
## 645               77.82220
## 646               77.69870
## 655               73.47745
## 658               75.16755
## 665               78.31526
## 673               72.62548
## 686               75.09786
## 698               73.70544
## 699               73.60374
## 701               70.42455
## 720               69.32613
## 729               67.36773
## 732               61.40362
## 751               80.82148
## 752               78.17081
## 758               60.87117
## 760               60.99628
## 767               55.53712
## 771               73.79577
## 774               73.51803
## 788               74.49812
## 798               69.11399
## 807               73.15087
## 816               71.43912
## 822               73.80801
## 823               70.91990
## 825               73.08415
## 835               58.14052
## 840               60.00250
## 847               60.63093
## 853               61.77587
## 858               60.54889
## 859               60.20245
## 864               50.55978
## 872               78.84691
## 876               78.15175
## 878               76.40616
## 881               76.24750
## 884               63.57263
## 894               51.53570
## 898               47.13868
## 899               76.82966
## 902               73.23901
## 904               75.70512
## 906               75.39871
## 911               73.75797
## 922               79.72354
## 925               81.44363
## 926               82.35267
## 931               80.03631
## 934               79.14505
## 935               75.98008
## 954               63.04209
## 958               58.31915
## 960               58.73982
## 961               60.10887
## 971               63.11651
## 978               58.00881
## 979               75.13463
## 988               72.63442
## 991               70.23069
## 994               61.26336
## 997               79.69504
## 1002              82.26923
## 1006              81.03734
## 1011              68.41131
## 1014              68.26109
## 1022              57.74325
## 1027              78.55835
## 1035              80.73031
## 1036              78.53457
## 1039              78.33173
## 1041              74.28273
## 1047              75.16422
## 1050              70.53398
## 1051              69.95496
## 1058              68.78202
## 1062              71.07574
## 1066              70.47418
## 1074              62.47697
## 1079              60.55660
## 1080              59.23459
## 1089              53.88346
## 1093              60.95098
## 1094              60.39188
## 1096              60.20381
## 1099              59.30881
## 1103              50.81755
## 1105              53.95771
## 1111              69.93443
## 1115              67.26981
## 1118              67.59675
## 1119              64.09032
## 1124              63.23573
## 1137              58.44968
## 1139              71.57311
## 1141              71.70188
## 1146              70.35454
## 1147              70.04827
## 1152              66.25270
## 1157              78.40419
## 1158              78.33952
## 1161              78.39339
## 1164              78.02829
## 1166              76.69982
## 1168              75.57420
## 1171              81.03301
## 1172              74.56610
## 1175              78.58271
## 1176              83.05251
## 1178              83.54917
## 1180              80.49704
## 1187              66.26556
## 1199              59.87945
## 1200              59.50136
## 1210              68.12472
## 1213              66.85990
## 1215              64.38125
## 1226              72.58774
## 1228              71.69277
## 1230              71.89069
## 1232              71.80676
## 1234              71.35785
## 1237              67.77436
## 1242              69.09360
## 1251              81.19967
## 1252              81.28612
## 1271              80.21750
## 1273              79.13731
## 1282              76.91238
## 1290              77.66703
## 1302              72.90244
## 1308              72.56794
## 1322              78.69540
## 1329              76.79247
## 1343              74.12769
## 1350              74.04066
## 1355              75.63821
## 1365              64.80960
## 1367              65.80459
## 1372              54.29529
## 1375              52.81261
## 1384              73.03275
## 1391              58.69375
## 1392              67.13245
## 1396              73.59863
## 1404              78.17953
## 1413              72.24351
## 1415              71.51715
## 1417              69.69562
## 1420              71.36071
## 1425              70.98457
## 1433              64.18093
## 1445              73.68290
## 1453              77.81824
## 1458              74.78913
## 1463              74.17268
## 1466              72.57477
## 1470              65.27684
## 1471              68.70382
## 1479              59.75653
## 1483              46.33876
## 1491              62.47954
## 1499              60.20582
## 1505              58.61493
## 1511              71.59448
## 1513              75.40465
## 1515              75.66649
## 1518              75.75766
## 1519              76.54564
## 1522              76.07329
## 1526              76.02355
## 1531              78.75529
## 1535              76.00141
## 1537              74.90244
## 1540              79.90152
## 1542              75.21847
## 1543              83.01678
## 1549              77.05971
## 1551              80.23258
## 1553              79.22638
## 1567              61.73791
## 1572              62.99773
## 1573              62.03671
## 1581              48.60083
## 1582              48.89026
## 1586              46.51233
## 1589              72.87261
## 1593              72.83679
## 1597              70.86304
## 1607              70.22864
## 1618              68.08147
## 1633              54.93383
## 1639              79.20711
## 1649              75.36990
## 1650              75.30957
## 1659              62.13795
## 1666              61.71266
## 1674              72.20605
## 1676              73.04926
## 1678              72.32636
## 1687              74.36244
## 1690              74.77862
## 1691              74.53251
## 1693              74.60022
## 1698              72.27944
## 1703              72.01464
## 1708              71.01234
## 1709              70.33681
## 1714              69.75453
## 1723              73.78950
## 1725              72.89679
## 1727              71.59880
## 1734              77.11375
## 1738              76.90174
## 1743              74.22899
## 1748              57.37613
## 1760              69.21279
## 1763              67.57486
## 1764              67.03758
## 1766              61.84943
## 1776              50.89472
## 1777              50.88194
## 1784              64.87114
## 1788              63.29281
## 1795              60.68464
## 1799              68.61444
## 1801              64.09670
## 1818              67.09049
## 1826              62.29334
## 1832              82.07041
## 1833              78.87920
## 1848              85.17440
## 1854              80.78893
## 1856              80.42205
## 1858              74.38904
## 1861              75.64667
## 1862              71.68335
## 1868              71.56586
## 1878              58.68658
## 1885              56.37659
## 1890              52.65918
## 1894              61.45545
## 1898              59.92259
## 1905              56.13090
## 1911              80.58332
## 1913              76.49710
## 1916              85.18931
## 1917              79.10854
## 1919              85.12569
## 1928              74.87271
## 1933              74.54710
## 1936              69.73593
## 1940              72.36344
## 1942              65.11809
## 1943              63.00037
## 1944              62.62807
## 1957              57.33968
## 1960              73.65427
## 1962              70.84298
## 1965              74.88055
## 1968              72.50552
## 1972              73.94457
## 1973              73.79222
## 1978              64.72270
## 1981              65.94672
## 1982              65.95549
## 1987              60.46708
## 1988              62.49506
## 1989              61.52545
## 1990              60.92447
## 1992              69.31676
## 1997              72.23169
## 2013              73.21732
## 2023              73.41486
## 2028              70.12424
## 2034              66.29734
## 2044              78.10016
## 2047              75.47164
## 2058              76.84383
## 2059              78.26930
## 2063              79.34257
## 2064              76.95182
## 2066              78.10807
## 2069              78.27846
## 2070              75.32316
## 2073              78.51540
## 2083              77.87655
## 2086              74.48572
## 2092              70.38743
## 2094              71.52612
## 2095              71.40956
## 2097              71.73391
## 2103              71.53259
## 2105              68.41266
## 2109              65.87473
## 2114              72.74333
## 2124              74.98463
## 2125              77.60856
## 2135              72.43028
## 2153              65.59041
## 2154              66.40000
## 2157              64.86293
## 2167              49.14686
## 2176              72.57166
## 2178              69.27872
## 2180              71.48630
## 2181              67.44653
## 2183              72.17232
## 2200              64.83381
## 2203              73.12338
## 2211              70.99750
## 2220              69.24064
## 2221              67.56516
## 2227              66.85452
## 2232              61.48365
## 2239              76.17322
## 2248              73.77452
## 2249              73.41836
## 2256              62.19828
## 2258              60.76470
## 2268              76.19613
## 2271              75.11156
## 2278              73.47617
## 2279              73.93394
## 2281              72.22735
## 2287              71.89170
## 2290              73.67132
## 2299              63.73075
## 2306              58.80776
## 2310              59.31357
## 2316              76.95273
## 2317              79.34366
## 2323              74.60529
## 2331              76.97082
## 2340              75.47058
## 2341              75.21769
## 2342              74.94700
## 2354              80.30245
## 2362              67.13412
## 2366              69.22966
## 2367              64.28314
## 2371              67.72325
## 2372              63.32371
## 2373              62.45839
## 2376              64.73930
## 2377              64.51155
## 2382              66.06369
## 2387              63.37454
## 2393              64.92647
## 2399              63.64869
## 2408              50.94562
## 2413              58.69565
## 2422              54.47104
## 2424              54.81082
## 2431              79.01508
## 2433              80.99679
## 2434              78.34870
## 2435              80.36267
## 2439              77.58031
## 2443              71.32606
## 2444              71.06977
## 2445              70.86095
## 2457              69.24783
## 2465              64.51969
## 2477              73.06932
## 2482              71.59111
## 2487              63.62545
## 2488              62.76460
## 2491              65.41498
## 2493              60.06364
## 2501              32.37364
## 2502              29.73596
## 2510              82.82797
## 2512              78.56581
## 2514              81.43518
## 2516              78.53064
## 2518              80.55357
## 2521              79.90662
## 2526              84.74632
## 2534              77.38800
## 2536              79.90994
## 2546              65.75181
## 2547              66.41709
## 2551              68.63684
## 2552              68.26154
## 2553              68.27699
## 2555              69.52503
## 2560              69.50428
## 2571              73.61388
## 2573              71.95163
## 2581              70.16864
## 2589              74.18295
## 2604              67.28655
## 2605              68.29719
## 2607              67.00868
## 2611              64.02532
## 2622              65.20485
## 2628              59.34435
## 2629              60.39302
## 2637              74.34492
## 2640              73.68696
## 2643              72.33173
## 2664              70.84211
## 2669              75.52914
## 2675              74.72938
## 2677              73.80591
## 2683              76.61679
## 2686              76.08326
## 2691              65.48771
## 2695              69.80535
## 2697              70.64635
## 2703              66.20598
## 2716              63.38088
## 2720              57.01987
## 2721              60.29151
## 2724              57.95186
## 2729              55.39864
## 2736              72.64951
## 2740              74.19290
## 2741              74.58381
## 2748              77.80506
## 2755              76.49140
## 2761              73.53041
## 2762              73.28412
## 2776              73.03037
## 2779              69.97188
## 2805              73.59070
## 2811              77.99801
## 2813              77.97801
## 2823              75.90697
## 2825              75.67820
## 2831              72.05558
## 2832              69.71685
## 2834              70.50965
## 2836              70.49518
## 2841              69.43840
## 2848              68.82238
## 2850              68.60704
## 2853              63.80262
## 2857              59.99712
## 2863              74.03634
## 2871              70.94285
## 2875              69.86667
## 2877              67.44417
## 2878              69.27001
## 2899              64.67498
## 2902              63.74487
## 2908              66.24860
## 2912              60.22454
## 2913              61.28320
## 2920              52.54212
## 2926              59.70816
## 2931              48.10812
## 2938              35.02091
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = sw.select.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 4.521186
# RMSE of Original Model
original.model_Preds = predict(original.model, newdata = validate)
as.data.frame(original.model_Preds)
##      original.model_Preds
## 1                62.00698
## 6                62.67364
## 7                62.04103
## 9                61.01874
## 10               60.33392
## 24               73.07173
## 28               71.69674
## 33               75.14697
## 35               75.12585
## 36               74.89521
## 42               71.83871
## 43               70.69296
## 48               68.97695
## 49               63.32559
## 57               60.86067
## 59               57.83462
## 60               54.72531
## 79               56.62073
## 80               56.36307
## 82               79.26422
## 105              69.32738
## 108              70.84764
## 115              87.02190
## 124              79.60654
## 129              80.29086
## 130              82.27297
## 136              78.69301
## 137              78.55665
## 151              71.00995
## 156              69.65243
## 157              69.24162
## 159              68.31973
## 164              75.02957
## 168              71.50002
## 174              73.61487
## 176              67.22297
## 182              72.51296
## 184              75.28874
## 186              75.11793
## 190              74.27687
## 193              66.74529
## 194              65.92339
## 201              63.72919
## 204              64.46545
## 206              63.10321
## 209              77.12707
## 210              77.30458
## 213              76.85851
## 218              75.22636
## 221              71.42882
## 223              73.72552
## 226              77.98855
## 232              76.90505
## 240              74.06419
## 242              81.49857
## 247              77.88112
## 258              70.74712
## 259              73.33693
## 264              72.74175
## 278              63.65791
## 285              60.82385
## 287              59.75891
## 288              59.67490
## 289              69.48890
## 296              62.15664
## 297              61.59028
## 298              61.10214
## 306              74.19989
## 307              73.76443
## 312              72.77488
## 318              71.73254
## 338              70.47342
## 339              69.61851
## 345              61.47979
## 351              42.26194
## 356              75.89389
## 368              74.28658
## 371              77.73112
## 375              75.62909
## 386              76.94642
## 402              63.03660
## 406              59.24801
## 409              59.47797
## 415              51.43880
## 418              66.16018
## 419              65.96848
## 426              59.26433
## 429              55.47894
## 430              54.96734
## 446              60.26261
## 448              63.03957
## 450              69.92309
## 451              71.26610
## 452              70.66296
## 453              64.12711
## 459              68.09309
## 460              67.98012
## 465              68.03554
## 468              66.33096
## 478              59.34773
## 480              58.53252
## 482              64.42847
## 492              58.22442
## 493              58.00162
## 503              79.03000
## 505              79.06670
## 509              76.73309
## 511              79.17828
## 513              56.59818
## 516              55.69656
## 518              53.00241
## 523              50.30745
## 527              44.82418
## 532              54.81944
## 537              53.35365
## 545              78.97759
## 555              76.27597
## 556              75.60251
## 559              75.25089
## 577              74.05325
## 580              74.11869
## 596              66.45840
## 601              63.70302
## 603              63.56949
## 614              63.23040
## 626              72.19975
## 627              75.34698
## 635              73.33795
## 642              77.60383
## 645              77.71974
## 646              77.64840
## 655              74.15987
## 658              75.40376
## 665              77.32856
## 673              72.48831
## 686              75.28485
## 698              74.02711
## 699              73.93498
## 701              70.78294
## 720              69.23909
## 729              66.77113
## 732              58.24646
## 751              81.07635
## 752              78.58716
## 758              61.79371
## 760              60.94184
## 767              55.28759
## 771              73.45352
## 774              72.81279
## 788              74.59469
## 798              69.74835
## 807              72.80599
## 816              71.12206
## 822              73.36111
## 823              70.54371
## 825              72.72513
## 835              58.18743
## 840              59.56793
## 847              59.72913
## 853              60.96616
## 858              60.47989
## 859              60.12506
## 864              51.62778
## 872              78.77644
## 876              78.33492
## 878              76.94945
## 881              75.65808
## 884              63.12480
## 894              52.04901
## 898              47.49345
## 899              76.54465
## 902              72.43819
## 904              75.14628
## 906              74.71222
## 911              73.03611
## 922              79.90315
## 925              81.81350
## 926              82.72348
## 931              80.95208
## 934              79.78115
## 935              76.39152
## 954              63.48762
## 958              57.66116
## 960              59.00861
## 961              59.55279
## 971              62.82329
## 978              57.28434
## 979              74.85484
## 988              72.93272
## 991              70.68529
## 994              61.34591
## 997              80.25853
## 1002             81.13120
## 1006             79.95248
## 1011             68.36062
## 1014             67.78846
## 1022             57.80672
## 1027             79.40251
## 1035             81.00013
## 1036             79.03603
## 1039             78.38359
## 1041             74.28005
## 1047             75.68321
## 1050             69.84834
## 1051             69.47264
## 1058             68.25827
## 1062             70.52581
## 1066             70.00426
## 1074             62.04208
## 1079             60.54241
## 1080             59.20801
## 1089             53.56951
## 1093             61.92047
## 1094             61.29241
## 1096             60.45159
## 1099             59.54511
## 1103             51.93469
## 1105             54.76906
## 1111             69.76305
## 1115             67.16384
## 1118             68.58458
## 1119             64.44764
## 1124             64.35269
## 1137             58.77744
## 1139             71.26721
## 1141             71.79178
## 1146             70.41165
## 1147             70.05968
## 1152             66.26764
## 1157             78.73082
## 1158             78.68335
## 1161             78.41505
## 1164             78.14078
## 1166             77.52438
## 1168             76.46770
## 1171             80.83328
## 1172             74.92378
## 1175             80.65517
## 1176             83.27755
## 1178             84.10627
## 1180             80.57073
## 1187             65.26239
## 1199             59.60539
## 1200             59.40860
## 1210             67.93497
## 1213             66.88398
## 1215             64.14436
## 1226             72.48492
## 1228             71.51328
## 1230             71.70809
## 1232             71.40156
## 1234             70.77814
## 1237             67.20760
## 1242             68.23066
## 1251             80.96626
## 1252             81.41713
## 1271             80.14510
## 1273             79.65601
## 1282             76.89036
## 1290             78.68794
## 1302             73.17200
## 1308             71.89758
## 1322             78.12525
## 1329             76.15226
## 1343             74.30129
## 1350             73.65343
## 1355             74.95323
## 1365             64.62586
## 1367             65.61515
## 1372             54.12985
## 1375             52.70721
## 1384             72.08973
## 1391             59.76826
## 1392             67.16878
## 1396             73.65295
## 1404             78.08830
## 1413             72.06450
## 1415             71.38023
## 1417             69.61030
## 1420             71.27814
## 1425             70.60545
## 1433             63.88228
## 1445             73.89123
## 1453             77.83218
## 1458             74.59759
## 1463             73.79569
## 1466             73.18560
## 1470             64.83459
## 1471             68.36791
## 1479             60.26027
## 1483             46.37921
## 1491             62.80027
## 1499             61.17040
## 1505             59.46977
## 1511             71.68163
## 1513             74.96231
## 1515             75.20717
## 1518             75.64009
## 1519             75.93251
## 1522             75.21329
## 1526             76.01955
## 1531             78.61639
## 1535             76.78166
## 1537             75.77070
## 1540             81.65976
## 1542             75.02397
## 1543             84.44153
## 1549             77.00459
## 1551             80.59527
## 1553             79.17191
## 1567             60.98553
## 1572             63.96892
## 1573             61.68849
## 1581             49.98473
## 1582             49.22669
## 1586             47.00396
## 1589             72.49778
## 1593             72.09956
## 1597             70.05520
## 1607             70.03394
## 1618             68.23438
## 1633             55.92212
## 1639             79.07717
## 1649             75.63389
## 1650             75.52986
## 1659             61.58676
## 1666             61.44180
## 1674             71.62724
## 1676             72.39705
## 1678             71.76407
## 1687             74.51804
## 1690             74.32530
## 1691             74.30124
## 1693             74.00040
## 1698             72.39987
## 1703             72.75810
## 1708             71.57485
## 1709             70.90545
## 1714             69.86434
## 1723             73.59189
## 1725             72.69905
## 1727             71.54454
## 1734             76.55115
## 1738             76.68279
## 1743             74.15915
## 1748             56.67950
## 1760             68.67657
## 1763             67.08688
## 1764             66.42792
## 1766             61.87903
## 1776             50.72184
## 1777             50.53964
## 1784             64.31384
## 1788             62.90410
## 1795             60.86747
## 1799             68.32213
## 1801             65.99840
## 1818             67.45512
## 1826             62.71954
## 1832             84.42236
## 1833             81.19742
## 1848             84.75491
## 1854             81.07325
## 1856             80.75675
## 1858             74.19981
## 1861             75.49495
## 1862             72.14986
## 1868             71.44897
## 1878             58.93552
## 1885             56.68745
## 1890             52.30504
## 1894             61.07872
## 1898             59.31498
## 1905             55.97627
## 1911             80.45326
## 1913             77.16611
## 1916             85.54940
## 1917             80.00915
## 1919             85.36086
## 1928             74.31598
## 1933             73.72274
## 1936             69.12432
## 1940             71.41308
## 1942             64.48676
## 1943             63.21535
## 1944             62.24038
## 1957             58.23353
## 1960             73.46141
## 1962             70.79455
## 1965             74.70036
## 1968             72.90302
## 1972             73.90409
## 1973             73.84304
## 1978             64.94776
## 1981             65.38777
## 1982             65.45515
## 1987             60.65942
## 1988             62.45371
## 1989             61.45878
## 1990             60.91968
## 1992             69.68002
## 1997             72.35398
## 2013             73.46183
## 2023             73.02123
## 2028             69.51749
## 2034             65.96916
## 2044             78.30558
## 2047             76.86773
## 2058             77.02650
## 2059             78.89916
## 2063             79.55187
## 2064             77.59509
## 2066             78.31857
## 2069             78.34685
## 2070             75.40932
## 2073             80.39058
## 2083             77.58678
## 2086             73.70943
## 2092             70.55977
## 2094             71.67523
## 2095             71.50345
## 2097             71.74265
## 2103             70.87108
## 2105             68.00587
## 2109             67.00593
## 2114             73.35422
## 2124             76.25302
## 2125             77.29316
## 2135             72.33390
## 2153             66.71137
## 2154             66.63085
## 2157             65.47834
## 2167             49.56909
## 2176             73.04762
## 2178             69.65931
## 2180             71.77441
## 2181             67.86098
## 2183             72.43997
## 2200             64.09343
## 2203             72.59486
## 2211             70.49735
## 2220             69.45293
## 2221             68.62917
## 2227             67.27196
## 2232             62.17336
## 2239             75.50896
## 2248             72.99520
## 2249             72.59211
## 2256             63.55549
## 2258             61.43924
## 2268             75.17276
## 2271             74.25136
## 2278             73.60003
## 2279             74.24690
## 2281             73.54382
## 2287             72.52554
## 2290             73.04537
## 2299             65.46322
## 2306             58.52594
## 2310             60.63357
## 2316             76.25897
## 2317             79.34218
## 2323             74.22101
## 2331             77.57450
## 2340             75.87857
## 2341             75.55959
## 2342             75.08224
## 2354             80.32487
## 2362             66.76351
## 2366             68.74074
## 2367             64.29951
## 2371             67.51558
## 2372             64.36003
## 2373             62.30194
## 2376             64.44992
## 2377             64.79079
## 2382             65.67007
## 2387             63.29378
## 2393             64.78769
## 2399             63.29519
## 2408             51.10100
## 2413             58.06241
## 2422             53.72636
## 2424             54.07227
## 2431             79.39532
## 2433             81.00464
## 2434             78.64550
## 2435             80.28871
## 2439             78.00684
## 2443             71.69799
## 2444             71.48657
## 2445             71.28770
## 2457             68.98362
## 2465             64.50656
## 2477             72.66274
## 2482             71.08572
## 2487             63.21845
## 2488             62.65637
## 2491             65.11867
## 2493             59.58466
## 2501             31.57448
## 2502             30.78894
## 2510             82.90883
## 2512             78.86479
## 2514             81.79250
## 2516             78.77811
## 2518             80.74302
## 2521             79.88235
## 2526             84.51901
## 2534             76.61283
## 2536             78.81157
## 2546             66.10262
## 2547             66.01227
## 2551             68.38156
## 2552             68.01105
## 2553             68.05605
## 2555             70.42264
## 2560             69.53851
## 2571             73.03411
## 2573             71.29481
## 2581             69.65656
## 2589             74.09906
## 2604             67.61153
## 2605             67.67830
## 2607             66.48297
## 2611             63.67531
## 2622             65.24407
## 2628             59.54491
## 2629             60.66651
## 2637             74.38234
## 2640             74.83279
## 2643             71.78534
## 2664             70.22870
## 2669             75.25153
## 2675             74.29640
## 2677             73.38349
## 2683             76.23673
## 2686             75.35111
## 2691             65.69767
## 2695             70.03019
## 2697             69.73279
## 2703             64.76257
## 2716             63.51091
## 2720             58.20465
## 2721             60.93522
## 2724             59.02288
## 2729             55.59369
## 2736             72.86659
## 2740             74.43540
## 2741             74.60038
## 2748             77.74878
## 2755             76.20913
## 2761             72.72649
## 2762             72.44000
## 2776             73.39712
## 2779             69.88780
## 2805             74.90730
## 2811             77.88440
## 2813             78.27957
## 2823             75.74780
## 2825             75.55056
## 2831             71.82741
## 2832             69.47918
## 2834             71.17256
## 2836             70.52318
## 2841             69.54837
## 2848             68.08558
## 2850             67.78178
## 2853             62.79227
## 2857             59.15016
## 2863             74.00885
## 2871             70.78678
## 2875             69.98561
## 2877             67.80600
## 2878             69.55786
## 2899             64.38566
## 2902             63.25688
## 2908             65.78477
## 2912             59.57095
## 2913             60.91770
## 2920             52.40302
## 2926             59.78845
## 2931             48.02131
## 2938             34.90615
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = original.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 4.548685
# RMSE of Poly2Log Model
poly2logmodel_Preds = predict(poly2logmodel, newdata = validate)
as.data.frame(poly2logmodel_Preds)
##      poly2logmodel_Preds
## 1               65.36285
## 6               65.04255
## 7               64.57153
## 9               64.07558
## 10              63.57594
## 24              75.15340
## 28              74.49068
## 33              75.77933
## 35              74.73490
## 36              74.68665
## 42              72.62916
## 43              69.86209
## 48              69.97629
## 49              59.53415
## 57              57.65260
## 59              56.91763
## 60              57.43848
## 79              68.29692
## 80              67.99165
## 82              80.00336
## 105             73.56737
## 108             72.97306
## 115             83.84505
## 124             82.45711
## 129             79.09504
## 130             79.48500
## 136             76.26041
## 137             76.27300
## 151             71.50479
## 156             69.37623
## 157             69.71964
## 159             68.41937
## 164             73.99311
## 168             74.78687
## 174             74.64601
## 176             68.77127
## 182             75.66910
## 184             75.74653
## 186             75.71337
## 190             75.01001
## 193             70.50388
## 194             68.94431
## 201             67.91196
## 204             68.89757
## 206             65.57496
## 209             77.69239
## 210             77.53767
## 213             77.11635
## 218             75.52773
## 221             70.60495
## 223             68.79800
## 226             76.74264
## 232             75.42076
## 240             74.11138
## 242             79.62985
## 247             79.08562
## 258             72.84780
## 259             73.15668
## 264             74.15598
## 278             58.90128
## 285             56.39172
## 287             56.08597
## 288             56.36596
## 289             68.23991
## 296             61.39419
## 297             61.92013
## 298             61.65784
## 306             75.85674
## 307             75.22626
## 312             72.02436
## 318             72.29254
## 338             63.23719
## 339             60.99163
## 345             58.61322
## 351             54.48637
## 356             76.81192
## 368             76.07938
## 371             76.59082
## 375             75.88854
## 386             75.94112
## 402             60.90420
## 406             61.19793
## 409             58.76365
## 415             50.79987
## 418             62.59232
## 419             61.56918
## 426             56.50613
## 429             53.79469
## 430             53.56022
## 446             56.55637
## 448             56.83985
## 450             70.34551
## 451             70.14270
## 452             67.95593
## 453             66.91956
## 459             65.02777
## 460             65.37016
## 465             69.55411
## 468             64.36302
## 478             55.18980
## 480             53.30017
## 482             57.65236
## 492             53.45678
## 493             54.07134
## 503             79.63121
## 505             80.67652
## 509             79.50925
## 511             79.46527
## 513             52.87530
## 516             51.10272
## 518             50.79731
## 523             48.85853
## 527             50.61146
## 532             54.66459
## 537             51.60181
## 545             79.66309
## 555             77.43983
## 556             76.60600
## 559             77.28857
## 577             74.58519
## 580             75.30146
## 596             62.03666
## 601             65.80368
## 603             65.66422
## 614             57.61624
## 626             75.39633
## 627             75.72007
## 635             74.71675
## 642             78.08990
## 645             77.58596
## 646             77.19050
## 655             73.69398
## 658             76.11105
## 665             77.99008
## 673             74.17941
## 686             76.81145
## 698             73.97012
## 699             74.01068
## 701             73.45732
## 720             69.55470
## 729             61.38720
## 732             58.19061
## 751             80.12571
## 752             78.68092
## 758             56.85955
## 760             57.19318
## 767             53.03872
## 771             70.71457
## 774             69.86324
## 788             75.20178
## 798             69.77258
## 807             73.10832
## 816             72.11862
## 822             71.13176
## 823             70.52063
## 825             70.65935
## 835             56.51264
## 840             54.89046
## 847             57.48048
## 853             62.63218
## 858             59.80014
## 859             59.15821
## 864             51.44088
## 872             76.49477
## 876             75.18618
## 878             74.69076
## 881             75.33519
## 884             61.30860
## 894             52.79707
## 898             49.74979
## 899             77.22721
## 902             74.81497
## 904             75.87496
## 906             75.53618
## 911             73.81689
## 922             80.56039
## 925             80.89492
## 926             82.00550
## 931             80.75524
## 934             79.96054
## 935             79.15860
## 954             57.08582
## 958             55.11058
## 960             54.28534
## 961             55.02049
## 971             58.99159
## 978             57.92349
## 979             75.97328
## 988             74.19307
## 991             71.41419
## 994             65.38296
## 997             79.95217
## 1002            79.80209
## 1006            79.15642
## 1011            65.26283
## 1014            63.36983
## 1022            55.66507
## 1027            79.46687
## 1035            80.78548
## 1036            79.69687
## 1039            78.79284
## 1041            77.51639
## 1047            76.46570
## 1050            71.63639
## 1051            71.04601
## 1058            70.23765
## 1062            69.14854
## 1066            68.63565
## 1074            67.40803
## 1079            55.24686
## 1080            54.88630
## 1089            55.01669
## 1093            54.74538
## 1094            54.25291
## 1096            55.32681
## 1099            54.17412
## 1103            50.30225
## 1105            51.00763
## 1111            68.55036
## 1115            63.86326
## 1118            62.46780
## 1119            60.57282
## 1124            60.01234
## 1137            54.18087
## 1139            70.50397
## 1141            69.67113
## 1146            67.31252
## 1147            66.75425
## 1152            63.58881
## 1157            78.75479
## 1158            78.60366
## 1161            78.34458
## 1164            77.36230
## 1166            76.51831
## 1168            75.60326
## 1171            81.23760
## 1172            79.75934
## 1175            79.96260
## 1176            82.33061
## 1178            82.51633
## 1180            81.51172
## 1187            67.39080
## 1199            61.08870
## 1200            60.87914
## 1210            66.83594
## 1213            67.88944
## 1215            67.44605
## 1226            73.04880
## 1228            72.36076
## 1230            72.62885
## 1232            72.38625
## 1234            72.03076
## 1237            68.90902
## 1242            68.63457
## 1251            82.16561
## 1252            82.07166
## 1271            79.19135
## 1273            79.18464
## 1282            77.30669
## 1290            79.35242
## 1302            69.84888
## 1308            66.56688
## 1322            79.22749
## 1329            78.17281
## 1343            74.21580
## 1350            77.62766
## 1355            76.50115
## 1365            59.37025
## 1367            60.04142
## 1372            52.81547
## 1375            50.82195
## 1384            73.67408
## 1391            65.54119
## 1392            66.96738
## 1396            74.57534
## 1404            76.26940
## 1413            72.80982
## 1415            71.50321
## 1417            73.15401
## 1420            72.81368
## 1425            73.23601
## 1433            65.83066
## 1445            76.54398
## 1453            78.45476
## 1458            76.03037
## 1463            73.36020
## 1466            72.39761
## 1470            66.95293
## 1471            67.66549
## 1479            56.91685
## 1483            51.88719
## 1491            59.45380
## 1499            54.83838
## 1505            54.93741
## 1511            73.56118
## 1513            74.51287
## 1515            74.71853
## 1518            74.75980
## 1519            75.28303
## 1522            74.74668
## 1526            75.84655
## 1531            77.18502
## 1535            76.13435
## 1537            75.48656
## 1540            78.88769
## 1542            78.20594
## 1543            79.30010
## 1549            77.77980
## 1551            77.97250
## 1553            77.67891
## 1567            58.66633
## 1572            56.83529
## 1573            55.23537
## 1581            50.75468
## 1582            50.88396
## 1586            49.27009
## 1589            73.59522
## 1593            73.62788
## 1597            73.14137
## 1607            72.82539
## 1618            71.75491
## 1633            53.07771
## 1639            79.40319
## 1649            77.00841
## 1650            76.78079
## 1659            57.94167
## 1666            58.65878
## 1674            75.35048
## 1676            74.86129
## 1678            74.54481
## 1687            76.16327
## 1690            76.05390
## 1691            76.16257
## 1693            76.15480
## 1698            74.52745
## 1703            73.96819
## 1708            72.78940
## 1709            71.62192
## 1714            71.79002
## 1723            75.24458
## 1725            74.41353
## 1727            73.82537
## 1734            75.70600
## 1738            77.61464
## 1743            75.31121
## 1748            65.88058
## 1760            70.78410
## 1763            69.87710
## 1764            69.40873
## 1766            55.36656
## 1776            50.88001
## 1777            50.86492
## 1784            62.72696
## 1788            61.41031
## 1795            60.19517
## 1799            60.99879
## 1801            58.13598
## 1818            67.40385
## 1826            65.61186
## 1832            82.57702
## 1833            82.07143
## 1848            83.43555
## 1854            81.54683
## 1856            81.28123
## 1858            79.07295
## 1861            78.42670
## 1862            73.79637
## 1868            71.70007
## 1878            60.64877
## 1885            55.37112
## 1890            52.61720
## 1894            56.04322
## 1898            54.88220
## 1905            52.81084
## 1911            81.41852
## 1913            80.24967
## 1916            81.95790
## 1917            80.46941
## 1919            82.01928
## 1928            74.68506
## 1933            74.47882
## 1936            72.65232
## 1940            73.20363
## 1942            66.47158
## 1943            67.57527
## 1944            65.80757
## 1957            62.92699
## 1960            73.85796
## 1962            74.17796
## 1965            76.22421
## 1968            71.78379
## 1972            76.16312
## 1973            74.03274
## 1978            61.71004
## 1981            60.33010
## 1982            60.57749
## 1987            57.82872
## 1988            58.33144
## 1989            57.61545
## 1990            57.60556
## 1992            71.35454
## 1997            74.19150
## 2013            72.85783
## 2023            70.83928
## 2028            73.24052
## 2034            72.99517
## 2044            78.58750
## 2047            76.37051
## 2058            79.80083
## 2059            78.84506
## 2063            78.79821
## 2064            77.53272
## 2066            77.26810
## 2069            78.62387
## 2070            77.86107
## 2073            75.40782
## 2083            76.11660
## 2086            73.88888
## 2092            75.12233
## 2094            74.46614
## 2095            74.39979
## 2097            75.03093
## 2103            73.99501
## 2105            71.19793
## 2109            71.81766
## 2114            74.54117
## 2124            75.37228
## 2125            77.74724
## 2135            74.30055
## 2153            65.14648
## 2154            65.20816
## 2157            61.49394
## 2167            51.85972
## 2176            73.81467
## 2178            71.25844
## 2180            70.57970
## 2181            68.14025
## 2183            70.55800
## 2200            63.11184
## 2203            72.60637
## 2211            72.32554
## 2220            69.03982
## 2221            64.98852
## 2227            64.14739
## 2232            60.79124
## 2239            74.99567
## 2248            73.46745
## 2249            73.03622
## 2256            61.67465
## 2258            60.95151
## 2268            76.43792
## 2271            75.36668
## 2278            74.72811
## 2279            75.60905
## 2281            74.06250
## 2287            74.55079
## 2290            75.81230
## 2299            61.08206
## 2306            55.69103
## 2310            56.93909
## 2316            77.80976
## 2317            78.58515
## 2323            76.38819
## 2331            77.94135
## 2340            76.85232
## 2341            76.87114
## 2342            76.64147
## 2354            79.72118
## 2362            72.64387
## 2366            71.80706
## 2367            68.38340
## 2371            71.08510
## 2372            68.77401
## 2373            67.51534
## 2376            68.19068
## 2377            67.88946
## 2382            61.34600
## 2387            61.38671
## 2393            61.47270
## 2399            57.18471
## 2408            53.86808
## 2413            54.93225
## 2422            56.04085
## 2424            56.51490
## 2431            79.98573
## 2433            80.34702
## 2434            78.98351
## 2435            79.63864
## 2439            78.14410
## 2443            73.94768
## 2444            73.85914
## 2445            73.80544
## 2457            72.22228
## 2465            65.34800
## 2477            67.33926
## 2482            66.65024
## 2487            57.35935
## 2488            56.50260
## 2491            58.57560
## 2493            56.33145
## 2501            50.89404
## 2502            48.95950
## 2510            80.99026
## 2512            79.86687
## 2514            80.63407
## 2516            79.87535
## 2518            80.62376
## 2521            80.31691
## 2526            81.00702
## 2534            77.86487
## 2536            78.46888
## 2546            68.63360
## 2547            69.25685
## 2551            69.65846
## 2552            69.34732
## 2553            69.53944
## 2555            68.94708
## 2560            68.74060
## 2571            75.79362
## 2573            75.62126
## 2581            68.83205
## 2589            74.45050
## 2604            68.41235
## 2605            69.28158
## 2607            67.90513
## 2611            65.65429
## 2622            58.75733
## 2628            55.25533
## 2629            54.05078
## 2637            73.86940
## 2640            74.18828
## 2643            75.90395
## 2664            65.92786
## 2669            75.21351
## 2675            74.90331
## 2677            74.03319
## 2683            75.94349
## 2686            75.48790
## 2691            70.04140
## 2695            69.86840
## 2697            70.92398
## 2703            67.89668
## 2716            56.62387
## 2720            55.11144
## 2721            55.49390
## 2724            53.47347
## 2729            51.01863
## 2736            70.80682
## 2740            69.07944
## 2741            69.47736
## 2748            76.75885
## 2755            75.18894
## 2761            73.89355
## 2762            73.72997
## 2776            74.28485
## 2779            65.77646
## 2805            76.27514
## 2811            78.24547
## 2813            78.56469
## 2823            76.58712
## 2825            76.80081
## 2831            74.11609
## 2832            71.62497
## 2834            69.45426
## 2836            68.33655
## 2841            69.85779
## 2848            69.18885
## 2850            69.23409
## 2853            64.38059
## 2857            64.54653
## 2863            74.45297
## 2871            71.56684
## 2875            73.38086
## 2877            69.24940
## 2878            73.20412
## 2899            66.70666
## 2902            65.71903
## 2908            58.51361
## 2912            56.73322
## 2913            57.18364
## 2920            51.85048
## 2926            57.16869
## 2931            50.23588
## 2938            48.44372
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = poly2logmodel_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 3.80083
# RMSE of Poly7Log Model

poly7logmodel_Preds = predict(poly7logmodel, newdata = validate)
as.data.frame(poly7logmodel_Preds)
##      poly7logmodel_Preds
## 1               64.55388
## 6               64.63545
## 7               64.04218
## 9               63.61055
## 10              62.72954
## 24              73.89513
## 28              73.73148
## 33              75.42495
## 35              74.68598
## 36              74.53141
## 42              73.02623
## 43              70.81147
## 48              71.26674
## 49              59.46023
## 57              56.36704
## 59              52.21586
## 60              51.49338
## 79              68.47678
## 80              68.87456
## 82              80.45484
## 105             74.73570
## 108             73.30255
## 115             82.69919
## 124             79.75191
## 129             78.61779
## 130             79.29858
## 136             76.87916
## 137             77.13504
## 151             72.13667
## 156             70.41583
## 157             70.86806
## 159             69.80782
## 164             74.11020
## 168             76.10504
## 174             75.40978
## 176             69.40519
## 182             75.40450
## 184             75.39451
## 186             74.90823
## 190             74.23880
## 193             69.15356
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## 221             71.38613
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## 242             80.63174
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## 285             55.71715
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## 306             74.22900
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## 338             64.56090
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## 958             53.54413
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## 961             53.32122
## 971             58.27864
## 978             57.62422
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## 991             71.45069
## 994             65.98876
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## 1011            65.89747
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## 1080            56.25599
## 1089            54.36796
## 1093            55.55390
## 1094            54.97881
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## 1099            53.63370
## 1103            49.37665
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## 1115            65.00106
## 1118            63.76382
## 1119            63.54056
## 1124            59.64422
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## 1139            70.05630
## 1141            69.18265
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## 1147            67.25856
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## 1171            81.71577
## 1172            82.71695
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## 1176            82.17439
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## 1252            83.12381
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## 1302            69.38669
## 1308            66.03500
## 1322            77.42955
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## 1343            73.98742
## 1350            77.08429
## 1355            75.88588
## 1365            61.23604
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## 1372            53.18431
## 1375            50.54953
## 1384            69.76718
## 1391            66.79103
## 1392            68.75813
## 1396            75.60098
## 1404            76.38450
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## 1415            71.85375
## 1417            73.88723
## 1420            73.68057
## 1425            73.24581
## 1433            64.93813
## 1445            77.35747
## 1453            77.32605
## 1458            75.14067
## 1463            74.35198
## 1466            73.27406
## 1470            67.45238
## 1471            67.55541
## 1479            57.79741
## 1483            52.82901
## 1491            58.64953
## 1499            54.81282
## 1505            54.71435
## 1511            73.92437
## 1513            74.35615
## 1515            74.32855
## 1518            74.41979
## 1519            75.08966
## 1522            74.56037
## 1526            79.09298
## 1531            78.71249
## 1535            76.45027
## 1537            75.22929
## 1540            78.96682
## 1542            78.51249
## 1543            79.66123
## 1549            77.57930
## 1551            77.96556
## 1553            77.74372
## 1567            59.19826
## 1572            56.58998
## 1573            55.86759
## 1581            51.00974
## 1582            51.59518
## 1586            49.95097
## 1589            74.28251
## 1593            74.42089
## 1597            74.12798
## 1607            72.09948
## 1618            70.51460
## 1633            52.76605
## 1639            78.78208
## 1649            77.14765
## 1650            76.96212
## 1659            58.30494
## 1666            58.34048
## 1674            74.56776
## 1676            74.41961
## 1678            73.88261
## 1687            75.62485
## 1690            76.05292
## 1691            75.96177
## 1693            75.41371
## 1698            73.91166
## 1703            74.74411
## 1708            74.17788
## 1709            72.51461
## 1714            72.80204
## 1723            74.54476
## 1725            73.68211
## 1727            73.46771
## 1734            76.49781
## 1738            77.07299
## 1743            75.02015
## 1748            66.80643
## 1760            70.92936
## 1763            70.17346
## 1764            69.78079
## 1766            55.58541
## 1776            50.61119
## 1777            50.75469
## 1784            63.15899
## 1788            61.20300
## 1795            59.95413
## 1799            62.77078
## 1801            59.45621
## 1818            67.27385
## 1826            65.96814
## 1832            82.49201
## 1833            82.28968
## 1848            83.91822
## 1854            82.38192
## 1856            82.25161
## 1858            81.25552
## 1861            79.60954
## 1862            72.84998
## 1868            70.79369
## 1878            59.69363
## 1885            56.50435
## 1890            53.45345
## 1894            54.60068
## 1898            53.14073
## 1905            51.11173
## 1911            81.64296
## 1913            80.64420
## 1916            81.76426
## 1917            80.27417
## 1919            81.73070
## 1928            73.84989
## 1933            74.47364
## 1936            73.80763
## 1940            73.02916
## 1942            66.41513
## 1943            66.90658
## 1944            65.80882
## 1957            62.42586
## 1960            73.95283
## 1962            74.18736
## 1965            75.60071
## 1968            71.33033
## 1972            75.21473
## 1973            72.60308
## 1978            64.28664
## 1981            61.17774
## 1982            61.59453
## 1987            59.16360
## 1988            59.86541
## 1989            58.49395
## 1990            57.64666
## 1992            72.13434
## 1997            73.56926
## 2013            72.36938
## 2023            70.29383
## 2028            72.92075
## 2034            74.31516
## 2044            78.51938
## 2047            76.36893
## 2058            79.71069
## 2059            79.07012
## 2063            78.88595
## 2064            77.81097
## 2066            78.14771
## 2069            78.36820
## 2070            78.91584
## 2073            76.05812
## 2083            77.01755
## 2086            75.48049
## 2092            75.08168
## 2094            74.80244
## 2095            74.72315
## 2097            74.52518
## 2103            73.64836
## 2105            73.53675
## 2109            74.23780
## 2114            73.98495
## 2124            75.46036
## 2125            77.33286
## 2135            73.78829
## 2153            65.80740
## 2154            65.41298
## 2157            60.49330
## 2167            53.74004
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## 2178            74.10207
## 2180            72.53214
## 2181            72.07491
## 2183            71.45520
## 2200            62.95632
## 2203            70.35044
## 2211            71.47276
## 2220            69.53460
## 2221            65.78864
## 2227            63.28627
## 2232            61.16937
## 2239            75.65243
## 2248            73.83756
## 2249            73.71125
## 2256            61.22378
## 2258            61.35198
## 2268            76.40085
## 2271            75.76277
## 2278            74.25959
## 2279            74.69493
## 2281            73.10998
## 2287            73.93637
## 2290            75.11349
## 2299            61.27407
## 2306            56.04692
## 2310            55.96224
## 2316            77.65659
## 2317            78.34173
## 2323            76.88612
## 2331            77.65654
## 2340            75.84577
## 2341            75.64950
## 2342            75.71192
## 2354            79.39818
## 2362            72.69885
## 2366            71.32502
## 2367            70.79478
## 2371            70.65034
## 2372            70.57002
## 2373            69.78310
## 2376            69.31183
## 2377            69.07522
## 2382            60.22460
## 2387            60.16276
## 2393            58.33583
## 2399            57.35827
## 2408            54.99102
## 2413            55.40366
## 2422            57.17511
## 2424            57.63359
## 2431            80.15480
## 2433            80.44934
## 2434            79.55900
## 2435            79.97598
## 2439            78.45121
## 2443            72.10288
## 2444            71.92679
## 2445            71.78387
## 2457            71.12198
## 2465            65.33164
## 2477            67.30393
## 2482            66.68621
## 2487            57.44975
## 2488            56.97615
## 2491            59.44921
## 2493            57.99697
## 2501            51.64863
## 2502            49.71687
## 2510            79.44654
## 2512            78.35070
## 2514            78.96855
## 2516            78.17836
## 2518            78.53262
## 2521            78.16587
## 2526            80.20859
## 2534            77.99369
## 2536            78.65321
## 2546            69.88633
## 2547            70.47008
## 2551            70.70345
## 2552            70.27874
## 2553            70.64480
## 2555            70.14597
## 2560            70.46214
## 2571            74.84791
## 2573            74.64625
## 2581            67.48463
## 2589            74.71491
## 2604            68.35087
## 2605            69.20243
## 2607            67.98273
## 2611            66.21197
## 2622            59.02596
## 2628            56.72897
## 2629            54.22458
## 2637            70.95952
## 2640            73.18066
## 2643            76.81953
## 2664            66.98731
## 2669            74.75214
## 2675            73.55875
## 2677            73.34678
## 2683            76.40791
## 2686            75.79071
## 2691            73.52544
## 2695            70.52959
## 2697            71.61571
## 2703            68.27533
## 2716            56.85926
## 2720            55.39658
## 2721            55.46634
## 2724            53.79690
## 2729            51.57261
## 2736            69.75599
## 2740            68.25437
## 2741            68.82526
## 2748            76.60273
## 2755            75.52542
## 2761            74.33838
## 2762            74.16046
## 2776            75.69274
## 2779            64.99686
## 2805            76.60897
## 2811            78.32349
## 2813            78.39176
## 2823            76.00323
## 2825            75.95617
## 2831            73.75896
## 2832            71.86211
## 2834            69.80728
## 2836            69.37073
## 2841            70.30206
## 2848            69.86345
## 2850            70.18138
## 2853            65.55920
## 2857            66.20383
## 2863            74.39547
## 2871            71.60304
## 2875            71.71012
## 2877            67.90915
## 2878            71.68078
## 2899            67.90733
## 2902            66.97416
## 2908            58.49287
## 2912            59.32643
## 2913            58.02214
## 2920            52.07851
## 2926            57.94492
## 2931            51.05890
## 2938            49.20722
MSPE = data.frame(Observed = validate$Life.expectancy, Predicted = poly7logmodel_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 3.734417
# RMSE of Original with Interaction Model
interaction.model_Preds = predict(interaction.model, newdata = validate)
as.data.frame(original.model_Preds)
##      original.model_Preds
## 1                62.00698
## 6                62.67364
## 7                62.04103
## 9                61.01874
## 10               60.33392
## 24               73.07173
## 28               71.69674
## 33               75.14697
## 35               75.12585
## 36               74.89521
## 42               71.83871
## 43               70.69296
## 48               68.97695
## 49               63.32559
## 57               60.86067
## 59               57.83462
## 60               54.72531
## 79               56.62073
## 80               56.36307
## 82               79.26422
## 105              69.32738
## 108              70.84764
## 115              87.02190
## 124              79.60654
## 129              80.29086
## 130              82.27297
## 136              78.69301
## 137              78.55665
## 151              71.00995
## 156              69.65243
## 157              69.24162
## 159              68.31973
## 164              75.02957
## 168              71.50002
## 174              73.61487
## 176              67.22297
## 182              72.51296
## 184              75.28874
## 186              75.11793
## 190              74.27687
## 193              66.74529
## 194              65.92339
## 201              63.72919
## 204              64.46545
## 206              63.10321
## 209              77.12707
## 210              77.30458
## 213              76.85851
## 218              75.22636
## 221              71.42882
## 223              73.72552
## 226              77.98855
## 232              76.90505
## 240              74.06419
## 242              81.49857
## 247              77.88112
## 258              70.74712
## 259              73.33693
## 264              72.74175
## 278              63.65791
## 285              60.82385
## 287              59.75891
## 288              59.67490
## 289              69.48890
## 296              62.15664
## 297              61.59028
## 298              61.10214
## 306              74.19989
## 307              73.76443
## 312              72.77488
## 318              71.73254
## 338              70.47342
## 339              69.61851
## 345              61.47979
## 351              42.26194
## 356              75.89389
## 368              74.28658
## 371              77.73112
## 375              75.62909
## 386              76.94642
## 402              63.03660
## 406              59.24801
## 409              59.47797
## 415              51.43880
## 418              66.16018
## 419              65.96848
## 426              59.26433
## 429              55.47894
## 430              54.96734
## 446              60.26261
## 448              63.03957
## 450              69.92309
## 451              71.26610
## 452              70.66296
## 453              64.12711
## 459              68.09309
## 460              67.98012
## 465              68.03554
## 468              66.33096
## 478              59.34773
## 480              58.53252
## 482              64.42847
## 492              58.22442
## 493              58.00162
## 503              79.03000
## 505              79.06670
## 509              76.73309
## 511              79.17828
## 513              56.59818
## 516              55.69656
## 518              53.00241
## 523              50.30745
## 527              44.82418
## 532              54.81944
## 537              53.35365
## 545              78.97759
## 555              76.27597
## 556              75.60251
## 559              75.25089
## 577              74.05325
## 580              74.11869
## 596              66.45840
## 601              63.70302
## 603              63.56949
## 614              63.23040
## 626              72.19975
## 627              75.34698
## 635              73.33795
## 642              77.60383
## 645              77.71974
## 646              77.64840
## 655              74.15987
## 658              75.40376
## 665              77.32856
## 673              72.48831
## 686              75.28485
## 698              74.02711
## 699              73.93498
## 701              70.78294
## 720              69.23909
## 729              66.77113
## 732              58.24646
## 751              81.07635
## 752              78.58716
## 758              61.79371
## 760              60.94184
## 767              55.28759
## 771              73.45352
## 774              72.81279
## 788              74.59469
## 798              69.74835
## 807              72.80599
## 816              71.12206
## 822              73.36111
## 823              70.54371
## 825              72.72513
## 835              58.18743
## 840              59.56793
## 847              59.72913
## 853              60.96616
## 858              60.47989
## 859              60.12506
## 864              51.62778
## 872              78.77644
## 876              78.33492
## 878              76.94945
## 881              75.65808
## 884              63.12480
## 894              52.04901
## 898              47.49345
## 899              76.54465
## 902              72.43819
## 904              75.14628
## 906              74.71222
## 911              73.03611
## 922              79.90315
## 925              81.81350
## 926              82.72348
## 931              80.95208
## 934              79.78115
## 935              76.39152
## 954              63.48762
## 958              57.66116
## 960              59.00861
## 961              59.55279
## 971              62.82329
## 978              57.28434
## 979              74.85484
## 988              72.93272
## 991              70.68529
## 994              61.34591
## 997              80.25853
## 1002             81.13120
## 1006             79.95248
## 1011             68.36062
## 1014             67.78846
## 1022             57.80672
## 1027             79.40251
## 1035             81.00013
## 1036             79.03603
## 1039             78.38359
## 1041             74.28005
## 1047             75.68321
## 1050             69.84834
## 1051             69.47264
## 1058             68.25827
## 1062             70.52581
## 1066             70.00426
## 1074             62.04208
## 1079             60.54241
## 1080             59.20801
## 1089             53.56951
## 1093             61.92047
## 1094             61.29241
## 1096             60.45159
## 1099             59.54511
## 1103             51.93469
## 1105             54.76906
## 1111             69.76305
## 1115             67.16384
## 1118             68.58458
## 1119             64.44764
## 1124             64.35269
## 1137             58.77744
## 1139             71.26721
## 1141             71.79178
## 1146             70.41165
## 1147             70.05968
## 1152             66.26764
## 1157             78.73082
## 1158             78.68335
## 1161             78.41505
## 1164             78.14078
## 1166             77.52438
## 1168             76.46770
## 1171             80.83328
## 1172             74.92378
## 1175             80.65517
## 1176             83.27755
## 1178             84.10627
## 1180             80.57073
## 1187             65.26239
## 1199             59.60539
## 1200             59.40860
## 1210             67.93497
## 1213             66.88398
## 1215             64.14436
## 1226             72.48492
## 1228             71.51328
## 1230             71.70809
## 1232             71.40156
## 1234             70.77814
## 1237             67.20760
## 1242             68.23066
## 1251             80.96626
## 1252             81.41713
## 1271             80.14510
## 1273             79.65601
## 1282             76.89036
## 1290             78.68794
## 1302             73.17200
## 1308             71.89758
## 1322             78.12525
## 1329             76.15226
## 1343             74.30129
## 1350             73.65343
## 1355             74.95323
## 1365             64.62586
## 1367             65.61515
## 1372             54.12985
## 1375             52.70721
## 1384             72.08973
## 1391             59.76826
## 1392             67.16878
## 1396             73.65295
## 1404             78.08830
## 1413             72.06450
## 1415             71.38023
## 1417             69.61030
## 1420             71.27814
## 1425             70.60545
## 1433             63.88228
## 1445             73.89123
## 1453             77.83218
## 1458             74.59759
## 1463             73.79569
## 1466             73.18560
## 1470             64.83459
## 1471             68.36791
## 1479             60.26027
## 1483             46.37921
## 1491             62.80027
## 1499             61.17040
## 1505             59.46977
## 1511             71.68163
## 1513             74.96231
## 1515             75.20717
## 1518             75.64009
## 1519             75.93251
## 1522             75.21329
## 1526             76.01955
## 1531             78.61639
## 1535             76.78166
## 1537             75.77070
## 1540             81.65976
## 1542             75.02397
## 1543             84.44153
## 1549             77.00459
## 1551             80.59527
## 1553             79.17191
## 1567             60.98553
## 1572             63.96892
## 1573             61.68849
## 1581             49.98473
## 1582             49.22669
## 1586             47.00396
## 1589             72.49778
## 1593             72.09956
## 1597             70.05520
## 1607             70.03394
## 1618             68.23438
## 1633             55.92212
## 1639             79.07717
## 1649             75.63389
## 1650             75.52986
## 1659             61.58676
## 1666             61.44180
## 1674             71.62724
## 1676             72.39705
## 1678             71.76407
## 1687             74.51804
## 1690             74.32530
## 1691             74.30124
## 1693             74.00040
## 1698             72.39987
## 1703             72.75810
## 1708             71.57485
## 1709             70.90545
## 1714             69.86434
## 1723             73.59189
## 1725             72.69905
## 1727             71.54454
## 1734             76.55115
## 1738             76.68279
## 1743             74.15915
## 1748             56.67950
## 1760             68.67657
## 1763             67.08688
## 1764             66.42792
## 1766             61.87903
## 1776             50.72184
## 1777             50.53964
## 1784             64.31384
## 1788             62.90410
## 1795             60.86747
## 1799             68.32213
## 1801             65.99840
## 1818             67.45512
## 1826             62.71954
## 1832             84.42236
## 1833             81.19742
## 1848             84.75491
## 1854             81.07325
## 1856             80.75675
## 1858             74.19981
## 1861             75.49495
## 1862             72.14986
## 1868             71.44897
## 1878             58.93552
## 1885             56.68745
## 1890             52.30504
## 1894             61.07872
## 1898             59.31498
## 1905             55.97627
## 1911             80.45326
## 1913             77.16611
## 1916             85.54940
## 1917             80.00915
## 1919             85.36086
## 1928             74.31598
## 1933             73.72274
## 1936             69.12432
## 1940             71.41308
## 1942             64.48676
## 1943             63.21535
## 1944             62.24038
## 1957             58.23353
## 1960             73.46141
## 1962             70.79455
## 1965             74.70036
## 1968             72.90302
## 1972             73.90409
## 1973             73.84304
## 1978             64.94776
## 1981             65.38777
## 1982             65.45515
## 1987             60.65942
## 1988             62.45371
## 1989             61.45878
## 1990             60.91968
## 1992             69.68002
## 1997             72.35398
## 2013             73.46183
## 2023             73.02123
## 2028             69.51749
## 2034             65.96916
## 2044             78.30558
## 2047             76.86773
## 2058             77.02650
## 2059             78.89916
## 2063             79.55187
## 2064             77.59509
## 2066             78.31857
## 2069             78.34685
## 2070             75.40932
## 2073             80.39058
## 2083             77.58678
## 2086             73.70943
## 2092             70.55977
## 2094             71.67523
## 2095             71.50345
## 2097             71.74265
## 2103             70.87108
## 2105             68.00587
## 2109             67.00593
## 2114             73.35422
## 2124             76.25302
## 2125             77.29316
## 2135             72.33390
## 2153             66.71137
## 2154             66.63085
## 2157             65.47834
## 2167             49.56909
## 2176             73.04762
## 2178             69.65931
## 2180             71.77441
## 2181             67.86098
## 2183             72.43997
## 2200             64.09343
## 2203             72.59486
## 2211             70.49735
## 2220             69.45293
## 2221             68.62917
## 2227             67.27196
## 2232             62.17336
## 2239             75.50896
## 2248             72.99520
## 2249             72.59211
## 2256             63.55549
## 2258             61.43924
## 2268             75.17276
## 2271             74.25136
## 2278             73.60003
## 2279             74.24690
## 2281             73.54382
## 2287             72.52554
## 2290             73.04537
## 2299             65.46322
## 2306             58.52594
## 2310             60.63357
## 2316             76.25897
## 2317             79.34218
## 2323             74.22101
## 2331             77.57450
## 2340             75.87857
## 2341             75.55959
## 2342             75.08224
## 2354             80.32487
## 2362             66.76351
## 2366             68.74074
## 2367             64.29951
## 2371             67.51558
## 2372             64.36003
## 2373             62.30194
## 2376             64.44992
## 2377             64.79079
## 2382             65.67007
## 2387             63.29378
## 2393             64.78769
## 2399             63.29519
## 2408             51.10100
## 2413             58.06241
## 2422             53.72636
## 2424             54.07227
## 2431             79.39532
## 2433             81.00464
## 2434             78.64550
## 2435             80.28871
## 2439             78.00684
## 2443             71.69799
## 2444             71.48657
## 2445             71.28770
## 2457             68.98362
## 2465             64.50656
## 2477             72.66274
## 2482             71.08572
## 2487             63.21845
## 2488             62.65637
## 2491             65.11867
## 2493             59.58466
## 2501             31.57448
## 2502             30.78894
## 2510             82.90883
## 2512             78.86479
## 2514             81.79250
## 2516             78.77811
## 2518             80.74302
## 2521             79.88235
## 2526             84.51901
## 2534             76.61283
## 2536             78.81157
## 2546             66.10262
## 2547             66.01227
## 2551             68.38156
## 2552             68.01105
## 2553             68.05605
## 2555             70.42264
## 2560             69.53851
## 2571             73.03411
## 2573             71.29481
## 2581             69.65656
## 2589             74.09906
## 2604             67.61153
## 2605             67.67830
## 2607             66.48297
## 2611             63.67531
## 2622             65.24407
## 2628             59.54491
## 2629             60.66651
## 2637             74.38234
## 2640             74.83279
## 2643             71.78534
## 2664             70.22870
## 2669             75.25153
## 2675             74.29640
## 2677             73.38349
## 2683             76.23673
## 2686             75.35111
## 2691             65.69767
## 2695             70.03019
## 2697             69.73279
## 2703             64.76257
## 2716             63.51091
## 2720             58.20465
## 2721             60.93522
## 2724             59.02288
## 2729             55.59369
## 2736             72.86659
## 2740             74.43540
## 2741             74.60038
## 2748             77.74878
## 2755             76.20913
## 2761             72.72649
## 2762             72.44000
## 2776             73.39712
## 2779             69.88780
## 2805             74.90730
## 2811             77.88440
## 2813             78.27957
## 2823             75.74780
## 2825             75.55056
## 2831             71.82741
## 2832             69.47918
## 2834             71.17256
## 2836             70.52318
## 2841             69.54837
## 2848             68.08558
## 2850             67.78178
## 2853             62.79227
## 2857             59.15016
## 2863             74.00885
## 2871             70.78678
## 2875             69.98561
## 2877             67.80600
## 2878             69.55786
## 2899             64.38566
## 2902             63.25688
## 2908             65.78477
## 2912             59.57095
## 2913             60.91770
## 2920             52.40302
## 2926             59.78845
## 2931             48.02131
## 2938             34.90615
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = interaction.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 4.369254
# RMSE of Poly2Log Model with interactions
poly2log.interaction.model_Preds = predict(poly2log.interaction.model, newdata = validate)
as.data.frame(poly2logmodel_Preds)
##      poly2logmodel_Preds
## 1               65.36285
## 6               65.04255
## 7               64.57153
## 9               64.07558
## 10              63.57594
## 24              75.15340
## 28              74.49068
## 33              75.77933
## 35              74.73490
## 36              74.68665
## 42              72.62916
## 43              69.86209
## 48              69.97629
## 49              59.53415
## 57              57.65260
## 59              56.91763
## 60              57.43848
## 79              68.29692
## 80              67.99165
## 82              80.00336
## 105             73.56737
## 108             72.97306
## 115             83.84505
## 124             82.45711
## 129             79.09504
## 130             79.48500
## 136             76.26041
## 137             76.27300
## 151             71.50479
## 156             69.37623
## 157             69.71964
## 159             68.41937
## 164             73.99311
## 168             74.78687
## 174             74.64601
## 176             68.77127
## 182             75.66910
## 184             75.74653
## 186             75.71337
## 190             75.01001
## 193             70.50388
## 194             68.94431
## 201             67.91196
## 204             68.89757
## 206             65.57496
## 209             77.69239
## 210             77.53767
## 213             77.11635
## 218             75.52773
## 221             70.60495
## 223             68.79800
## 226             76.74264
## 232             75.42076
## 240             74.11138
## 242             79.62985
## 247             79.08562
## 258             72.84780
## 259             73.15668
## 264             74.15598
## 278             58.90128
## 285             56.39172
## 287             56.08597
## 288             56.36596
## 289             68.23991
## 296             61.39419
## 297             61.92013
## 298             61.65784
## 306             75.85674
## 307             75.22626
## 312             72.02436
## 318             72.29254
## 338             63.23719
## 339             60.99163
## 345             58.61322
## 351             54.48637
## 356             76.81192
## 368             76.07938
## 371             76.59082
## 375             75.88854
## 386             75.94112
## 402             60.90420
## 406             61.19793
## 409             58.76365
## 415             50.79987
## 418             62.59232
## 419             61.56918
## 426             56.50613
## 429             53.79469
## 430             53.56022
## 446             56.55637
## 448             56.83985
## 450             70.34551
## 451             70.14270
## 452             67.95593
## 453             66.91956
## 459             65.02777
## 460             65.37016
## 465             69.55411
## 468             64.36302
## 478             55.18980
## 480             53.30017
## 482             57.65236
## 492             53.45678
## 493             54.07134
## 503             79.63121
## 505             80.67652
## 509             79.50925
## 511             79.46527
## 513             52.87530
## 516             51.10272
## 518             50.79731
## 523             48.85853
## 527             50.61146
## 532             54.66459
## 537             51.60181
## 545             79.66309
## 555             77.43983
## 556             76.60600
## 559             77.28857
## 577             74.58519
## 580             75.30146
## 596             62.03666
## 601             65.80368
## 603             65.66422
## 614             57.61624
## 626             75.39633
## 627             75.72007
## 635             74.71675
## 642             78.08990
## 645             77.58596
## 646             77.19050
## 655             73.69398
## 658             76.11105
## 665             77.99008
## 673             74.17941
## 686             76.81145
## 698             73.97012
## 699             74.01068
## 701             73.45732
## 720             69.55470
## 729             61.38720
## 732             58.19061
## 751             80.12571
## 752             78.68092
## 758             56.85955
## 760             57.19318
## 767             53.03872
## 771             70.71457
## 774             69.86324
## 788             75.20178
## 798             69.77258
## 807             73.10832
## 816             72.11862
## 822             71.13176
## 823             70.52063
## 825             70.65935
## 835             56.51264
## 840             54.89046
## 847             57.48048
## 853             62.63218
## 858             59.80014
## 859             59.15821
## 864             51.44088
## 872             76.49477
## 876             75.18618
## 878             74.69076
## 881             75.33519
## 884             61.30860
## 894             52.79707
## 898             49.74979
## 899             77.22721
## 902             74.81497
## 904             75.87496
## 906             75.53618
## 911             73.81689
## 922             80.56039
## 925             80.89492
## 926             82.00550
## 931             80.75524
## 934             79.96054
## 935             79.15860
## 954             57.08582
## 958             55.11058
## 960             54.28534
## 961             55.02049
## 971             58.99159
## 978             57.92349
## 979             75.97328
## 988             74.19307
## 991             71.41419
## 994             65.38296
## 997             79.95217
## 1002            79.80209
## 1006            79.15642
## 1011            65.26283
## 1014            63.36983
## 1022            55.66507
## 1027            79.46687
## 1035            80.78548
## 1036            79.69687
## 1039            78.79284
## 1041            77.51639
## 1047            76.46570
## 1050            71.63639
## 1051            71.04601
## 1058            70.23765
## 1062            69.14854
## 1066            68.63565
## 1074            67.40803
## 1079            55.24686
## 1080            54.88630
## 1089            55.01669
## 1093            54.74538
## 1094            54.25291
## 1096            55.32681
## 1099            54.17412
## 1103            50.30225
## 1105            51.00763
## 1111            68.55036
## 1115            63.86326
## 1118            62.46780
## 1119            60.57282
## 1124            60.01234
## 1137            54.18087
## 1139            70.50397
## 1141            69.67113
## 1146            67.31252
## 1147            66.75425
## 1152            63.58881
## 1157            78.75479
## 1158            78.60366
## 1161            78.34458
## 1164            77.36230
## 1166            76.51831
## 1168            75.60326
## 1171            81.23760
## 1172            79.75934
## 1175            79.96260
## 1176            82.33061
## 1178            82.51633
## 1180            81.51172
## 1187            67.39080
## 1199            61.08870
## 1200            60.87914
## 1210            66.83594
## 1213            67.88944
## 1215            67.44605
## 1226            73.04880
## 1228            72.36076
## 1230            72.62885
## 1232            72.38625
## 1234            72.03076
## 1237            68.90902
## 1242            68.63457
## 1251            82.16561
## 1252            82.07166
## 1271            79.19135
## 1273            79.18464
## 1282            77.30669
## 1290            79.35242
## 1302            69.84888
## 1308            66.56688
## 1322            79.22749
## 1329            78.17281
## 1343            74.21580
## 1350            77.62766
## 1355            76.50115
## 1365            59.37025
## 1367            60.04142
## 1372            52.81547
## 1375            50.82195
## 1384            73.67408
## 1391            65.54119
## 1392            66.96738
## 1396            74.57534
## 1404            76.26940
## 1413            72.80982
## 1415            71.50321
## 1417            73.15401
## 1420            72.81368
## 1425            73.23601
## 1433            65.83066
## 1445            76.54398
## 1453            78.45476
## 1458            76.03037
## 1463            73.36020
## 1466            72.39761
## 1470            66.95293
## 1471            67.66549
## 1479            56.91685
## 1483            51.88719
## 1491            59.45380
## 1499            54.83838
## 1505            54.93741
## 1511            73.56118
## 1513            74.51287
## 1515            74.71853
## 1518            74.75980
## 1519            75.28303
## 1522            74.74668
## 1526            75.84655
## 1531            77.18502
## 1535            76.13435
## 1537            75.48656
## 1540            78.88769
## 1542            78.20594
## 1543            79.30010
## 1549            77.77980
## 1551            77.97250
## 1553            77.67891
## 1567            58.66633
## 1572            56.83529
## 1573            55.23537
## 1581            50.75468
## 1582            50.88396
## 1586            49.27009
## 1589            73.59522
## 1593            73.62788
## 1597            73.14137
## 1607            72.82539
## 1618            71.75491
## 1633            53.07771
## 1639            79.40319
## 1649            77.00841
## 1650            76.78079
## 1659            57.94167
## 1666            58.65878
## 1674            75.35048
## 1676            74.86129
## 1678            74.54481
## 1687            76.16327
## 1690            76.05390
## 1691            76.16257
## 1693            76.15480
## 1698            74.52745
## 1703            73.96819
## 1708            72.78940
## 1709            71.62192
## 1714            71.79002
## 1723            75.24458
## 1725            74.41353
## 1727            73.82537
## 1734            75.70600
## 1738            77.61464
## 1743            75.31121
## 1748            65.88058
## 1760            70.78410
## 1763            69.87710
## 1764            69.40873
## 1766            55.36656
## 1776            50.88001
## 1777            50.86492
## 1784            62.72696
## 1788            61.41031
## 1795            60.19517
## 1799            60.99879
## 1801            58.13598
## 1818            67.40385
## 1826            65.61186
## 1832            82.57702
## 1833            82.07143
## 1848            83.43555
## 1854            81.54683
## 1856            81.28123
## 1858            79.07295
## 1861            78.42670
## 1862            73.79637
## 1868            71.70007
## 1878            60.64877
## 1885            55.37112
## 1890            52.61720
## 1894            56.04322
## 1898            54.88220
## 1905            52.81084
## 1911            81.41852
## 1913            80.24967
## 1916            81.95790
## 1917            80.46941
## 1919            82.01928
## 1928            74.68506
## 1933            74.47882
## 1936            72.65232
## 1940            73.20363
## 1942            66.47158
## 1943            67.57527
## 1944            65.80757
## 1957            62.92699
## 1960            73.85796
## 1962            74.17796
## 1965            76.22421
## 1968            71.78379
## 1972            76.16312
## 1973            74.03274
## 1978            61.71004
## 1981            60.33010
## 1982            60.57749
## 1987            57.82872
## 1988            58.33144
## 1989            57.61545
## 1990            57.60556
## 1992            71.35454
## 1997            74.19150
## 2013            72.85783
## 2023            70.83928
## 2028            73.24052
## 2034            72.99517
## 2044            78.58750
## 2047            76.37051
## 2058            79.80083
## 2059            78.84506
## 2063            78.79821
## 2064            77.53272
## 2066            77.26810
## 2069            78.62387
## 2070            77.86107
## 2073            75.40782
## 2083            76.11660
## 2086            73.88888
## 2092            75.12233
## 2094            74.46614
## 2095            74.39979
## 2097            75.03093
## 2103            73.99501
## 2105            71.19793
## 2109            71.81766
## 2114            74.54117
## 2124            75.37228
## 2125            77.74724
## 2135            74.30055
## 2153            65.14648
## 2154            65.20816
## 2157            61.49394
## 2167            51.85972
## 2176            73.81467
## 2178            71.25844
## 2180            70.57970
## 2181            68.14025
## 2183            70.55800
## 2200            63.11184
## 2203            72.60637
## 2211            72.32554
## 2220            69.03982
## 2221            64.98852
## 2227            64.14739
## 2232            60.79124
## 2239            74.99567
## 2248            73.46745
## 2249            73.03622
## 2256            61.67465
## 2258            60.95151
## 2268            76.43792
## 2271            75.36668
## 2278            74.72811
## 2279            75.60905
## 2281            74.06250
## 2287            74.55079
## 2290            75.81230
## 2299            61.08206
## 2306            55.69103
## 2310            56.93909
## 2316            77.80976
## 2317            78.58515
## 2323            76.38819
## 2331            77.94135
## 2340            76.85232
## 2341            76.87114
## 2342            76.64147
## 2354            79.72118
## 2362            72.64387
## 2366            71.80706
## 2367            68.38340
## 2371            71.08510
## 2372            68.77401
## 2373            67.51534
## 2376            68.19068
## 2377            67.88946
## 2382            61.34600
## 2387            61.38671
## 2393            61.47270
## 2399            57.18471
## 2408            53.86808
## 2413            54.93225
## 2422            56.04085
## 2424            56.51490
## 2431            79.98573
## 2433            80.34702
## 2434            78.98351
## 2435            79.63864
## 2439            78.14410
## 2443            73.94768
## 2444            73.85914
## 2445            73.80544
## 2457            72.22228
## 2465            65.34800
## 2477            67.33926
## 2482            66.65024
## 2487            57.35935
## 2488            56.50260
## 2491            58.57560
## 2493            56.33145
## 2501            50.89404
## 2502            48.95950
## 2510            80.99026
## 2512            79.86687
## 2514            80.63407
## 2516            79.87535
## 2518            80.62376
## 2521            80.31691
## 2526            81.00702
## 2534            77.86487
## 2536            78.46888
## 2546            68.63360
## 2547            69.25685
## 2551            69.65846
## 2552            69.34732
## 2553            69.53944
## 2555            68.94708
## 2560            68.74060
## 2571            75.79362
## 2573            75.62126
## 2581            68.83205
## 2589            74.45050
## 2604            68.41235
## 2605            69.28158
## 2607            67.90513
## 2611            65.65429
## 2622            58.75733
## 2628            55.25533
## 2629            54.05078
## 2637            73.86940
## 2640            74.18828
## 2643            75.90395
## 2664            65.92786
## 2669            75.21351
## 2675            74.90331
## 2677            74.03319
## 2683            75.94349
## 2686            75.48790
## 2691            70.04140
## 2695            69.86840
## 2697            70.92398
## 2703            67.89668
## 2716            56.62387
## 2720            55.11144
## 2721            55.49390
## 2724            53.47347
## 2729            51.01863
## 2736            70.80682
## 2740            69.07944
## 2741            69.47736
## 2748            76.75885
## 2755            75.18894
## 2761            73.89355
## 2762            73.72997
## 2776            74.28485
## 2779            65.77646
## 2805            76.27514
## 2811            78.24547
## 2813            78.56469
## 2823            76.58712
## 2825            76.80081
## 2831            74.11609
## 2832            71.62497
## 2834            69.45426
## 2836            68.33655
## 2841            69.85779
## 2848            69.18885
## 2850            69.23409
## 2853            64.38059
## 2857            64.54653
## 2863            74.45297
## 2871            71.56684
## 2875            73.38086
## 2877            69.24940
## 2878            73.20412
## 2899            66.70666
## 2902            65.71903
## 2908            58.51361
## 2912            56.73322
## 2913            57.18364
## 2920            51.85048
## 2926            57.16869
## 2931            50.23588
## 2938            48.44372
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = poly2log.interaction.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 3.671729
# RMSE of Poly7Log Model with interactions
poly7log.interaction.model_Preds = predict(poly7log.interaction.model, newdata = validate)
as.data.frame(poly2logmodel_Preds)
##      poly2logmodel_Preds
## 1               65.36285
## 6               65.04255
## 7               64.57153
## 9               64.07558
## 10              63.57594
## 24              75.15340
## 28              74.49068
## 33              75.77933
## 35              74.73490
## 36              74.68665
## 42              72.62916
## 43              69.86209
## 48              69.97629
## 49              59.53415
## 57              57.65260
## 59              56.91763
## 60              57.43848
## 79              68.29692
## 80              67.99165
## 82              80.00336
## 105             73.56737
## 108             72.97306
## 115             83.84505
## 124             82.45711
## 129             79.09504
## 130             79.48500
## 136             76.26041
## 137             76.27300
## 151             71.50479
## 156             69.37623
## 157             69.71964
## 159             68.41937
## 164             73.99311
## 168             74.78687
## 174             74.64601
## 176             68.77127
## 182             75.66910
## 184             75.74653
## 186             75.71337
## 190             75.01001
## 193             70.50388
## 194             68.94431
## 201             67.91196
## 204             68.89757
## 206             65.57496
## 209             77.69239
## 210             77.53767
## 213             77.11635
## 218             75.52773
## 221             70.60495
## 223             68.79800
## 226             76.74264
## 232             75.42076
## 240             74.11138
## 242             79.62985
## 247             79.08562
## 258             72.84780
## 259             73.15668
## 264             74.15598
## 278             58.90128
## 285             56.39172
## 287             56.08597
## 288             56.36596
## 289             68.23991
## 296             61.39419
## 297             61.92013
## 298             61.65784
## 306             75.85674
## 307             75.22626
## 312             72.02436
## 318             72.29254
## 338             63.23719
## 339             60.99163
## 345             58.61322
## 351             54.48637
## 356             76.81192
## 368             76.07938
## 371             76.59082
## 375             75.88854
## 386             75.94112
## 402             60.90420
## 406             61.19793
## 409             58.76365
## 415             50.79987
## 418             62.59232
## 419             61.56918
## 426             56.50613
## 429             53.79469
## 430             53.56022
## 446             56.55637
## 448             56.83985
## 450             70.34551
## 451             70.14270
## 452             67.95593
## 453             66.91956
## 459             65.02777
## 460             65.37016
## 465             69.55411
## 468             64.36302
## 478             55.18980
## 480             53.30017
## 482             57.65236
## 492             53.45678
## 493             54.07134
## 503             79.63121
## 505             80.67652
## 509             79.50925
## 511             79.46527
## 513             52.87530
## 516             51.10272
## 518             50.79731
## 523             48.85853
## 527             50.61146
## 532             54.66459
## 537             51.60181
## 545             79.66309
## 555             77.43983
## 556             76.60600
## 559             77.28857
## 577             74.58519
## 580             75.30146
## 596             62.03666
## 601             65.80368
## 603             65.66422
## 614             57.61624
## 626             75.39633
## 627             75.72007
## 635             74.71675
## 642             78.08990
## 645             77.58596
## 646             77.19050
## 655             73.69398
## 658             76.11105
## 665             77.99008
## 673             74.17941
## 686             76.81145
## 698             73.97012
## 699             74.01068
## 701             73.45732
## 720             69.55470
## 729             61.38720
## 732             58.19061
## 751             80.12571
## 752             78.68092
## 758             56.85955
## 760             57.19318
## 767             53.03872
## 771             70.71457
## 774             69.86324
## 788             75.20178
## 798             69.77258
## 807             73.10832
## 816             72.11862
## 822             71.13176
## 823             70.52063
## 825             70.65935
## 835             56.51264
## 840             54.89046
## 847             57.48048
## 853             62.63218
## 858             59.80014
## 859             59.15821
## 864             51.44088
## 872             76.49477
## 876             75.18618
## 878             74.69076
## 881             75.33519
## 884             61.30860
## 894             52.79707
## 898             49.74979
## 899             77.22721
## 902             74.81497
## 904             75.87496
## 906             75.53618
## 911             73.81689
## 922             80.56039
## 925             80.89492
## 926             82.00550
## 931             80.75524
## 934             79.96054
## 935             79.15860
## 954             57.08582
## 958             55.11058
## 960             54.28534
## 961             55.02049
## 971             58.99159
## 978             57.92349
## 979             75.97328
## 988             74.19307
## 991             71.41419
## 994             65.38296
## 997             79.95217
## 1002            79.80209
## 1006            79.15642
## 1011            65.26283
## 1014            63.36983
## 1022            55.66507
## 1027            79.46687
## 1035            80.78548
## 1036            79.69687
## 1039            78.79284
## 1041            77.51639
## 1047            76.46570
## 1050            71.63639
## 1051            71.04601
## 1058            70.23765
## 1062            69.14854
## 1066            68.63565
## 1074            67.40803
## 1079            55.24686
## 1080            54.88630
## 1089            55.01669
## 1093            54.74538
## 1094            54.25291
## 1096            55.32681
## 1099            54.17412
## 1103            50.30225
## 1105            51.00763
## 1111            68.55036
## 1115            63.86326
## 1118            62.46780
## 1119            60.57282
## 1124            60.01234
## 1137            54.18087
## 1139            70.50397
## 1141            69.67113
## 1146            67.31252
## 1147            66.75425
## 1152            63.58881
## 1157            78.75479
## 1158            78.60366
## 1161            78.34458
## 1164            77.36230
## 1166            76.51831
## 1168            75.60326
## 1171            81.23760
## 1172            79.75934
## 1175            79.96260
## 1176            82.33061
## 1178            82.51633
## 1180            81.51172
## 1187            67.39080
## 1199            61.08870
## 1200            60.87914
## 1210            66.83594
## 1213            67.88944
## 1215            67.44605
## 1226            73.04880
## 1228            72.36076
## 1230            72.62885
## 1232            72.38625
## 1234            72.03076
## 1237            68.90902
## 1242            68.63457
## 1251            82.16561
## 1252            82.07166
## 1271            79.19135
## 1273            79.18464
## 1282            77.30669
## 1290            79.35242
## 1302            69.84888
## 1308            66.56688
## 1322            79.22749
## 1329            78.17281
## 1343            74.21580
## 1350            77.62766
## 1355            76.50115
## 1365            59.37025
## 1367            60.04142
## 1372            52.81547
## 1375            50.82195
## 1384            73.67408
## 1391            65.54119
## 1392            66.96738
## 1396            74.57534
## 1404            76.26940
## 1413            72.80982
## 1415            71.50321
## 1417            73.15401
## 1420            72.81368
## 1425            73.23601
## 1433            65.83066
## 1445            76.54398
## 1453            78.45476
## 1458            76.03037
## 1463            73.36020
## 1466            72.39761
## 1470            66.95293
## 1471            67.66549
## 1479            56.91685
## 1483            51.88719
## 1491            59.45380
## 1499            54.83838
## 1505            54.93741
## 1511            73.56118
## 1513            74.51287
## 1515            74.71853
## 1518            74.75980
## 1519            75.28303
## 1522            74.74668
## 1526            75.84655
## 1531            77.18502
## 1535            76.13435
## 1537            75.48656
## 1540            78.88769
## 1542            78.20594
## 1543            79.30010
## 1549            77.77980
## 1551            77.97250
## 1553            77.67891
## 1567            58.66633
## 1572            56.83529
## 1573            55.23537
## 1581            50.75468
## 1582            50.88396
## 1586            49.27009
## 1589            73.59522
## 1593            73.62788
## 1597            73.14137
## 1607            72.82539
## 1618            71.75491
## 1633            53.07771
## 1639            79.40319
## 1649            77.00841
## 1650            76.78079
## 1659            57.94167
## 1666            58.65878
## 1674            75.35048
## 1676            74.86129
## 1678            74.54481
## 1687            76.16327
## 1690            76.05390
## 1691            76.16257
## 1693            76.15480
## 1698            74.52745
## 1703            73.96819
## 1708            72.78940
## 1709            71.62192
## 1714            71.79002
## 1723            75.24458
## 1725            74.41353
## 1727            73.82537
## 1734            75.70600
## 1738            77.61464
## 1743            75.31121
## 1748            65.88058
## 1760            70.78410
## 1763            69.87710
## 1764            69.40873
## 1766            55.36656
## 1776            50.88001
## 1777            50.86492
## 1784            62.72696
## 1788            61.41031
## 1795            60.19517
## 1799            60.99879
## 1801            58.13598
## 1818            67.40385
## 1826            65.61186
## 1832            82.57702
## 1833            82.07143
## 1848            83.43555
## 1854            81.54683
## 1856            81.28123
## 1858            79.07295
## 1861            78.42670
## 1862            73.79637
## 1868            71.70007
## 1878            60.64877
## 1885            55.37112
## 1890            52.61720
## 1894            56.04322
## 1898            54.88220
## 1905            52.81084
## 1911            81.41852
## 1913            80.24967
## 1916            81.95790
## 1917            80.46941
## 1919            82.01928
## 1928            74.68506
## 1933            74.47882
## 1936            72.65232
## 1940            73.20363
## 1942            66.47158
## 1943            67.57527
## 1944            65.80757
## 1957            62.92699
## 1960            73.85796
## 1962            74.17796
## 1965            76.22421
## 1968            71.78379
## 1972            76.16312
## 1973            74.03274
## 1978            61.71004
## 1981            60.33010
## 1982            60.57749
## 1987            57.82872
## 1988            58.33144
## 1989            57.61545
## 1990            57.60556
## 1992            71.35454
## 1997            74.19150
## 2013            72.85783
## 2023            70.83928
## 2028            73.24052
## 2034            72.99517
## 2044            78.58750
## 2047            76.37051
## 2058            79.80083
## 2059            78.84506
## 2063            78.79821
## 2064            77.53272
## 2066            77.26810
## 2069            78.62387
## 2070            77.86107
## 2073            75.40782
## 2083            76.11660
## 2086            73.88888
## 2092            75.12233
## 2094            74.46614
## 2095            74.39979
## 2097            75.03093
## 2103            73.99501
## 2105            71.19793
## 2109            71.81766
## 2114            74.54117
## 2124            75.37228
## 2125            77.74724
## 2135            74.30055
## 2153            65.14648
## 2154            65.20816
## 2157            61.49394
## 2167            51.85972
## 2176            73.81467
## 2178            71.25844
## 2180            70.57970
## 2181            68.14025
## 2183            70.55800
## 2200            63.11184
## 2203            72.60637
## 2211            72.32554
## 2220            69.03982
## 2221            64.98852
## 2227            64.14739
## 2232            60.79124
## 2239            74.99567
## 2248            73.46745
## 2249            73.03622
## 2256            61.67465
## 2258            60.95151
## 2268            76.43792
## 2271            75.36668
## 2278            74.72811
## 2279            75.60905
## 2281            74.06250
## 2287            74.55079
## 2290            75.81230
## 2299            61.08206
## 2306            55.69103
## 2310            56.93909
## 2316            77.80976
## 2317            78.58515
## 2323            76.38819
## 2331            77.94135
## 2340            76.85232
## 2341            76.87114
## 2342            76.64147
## 2354            79.72118
## 2362            72.64387
## 2366            71.80706
## 2367            68.38340
## 2371            71.08510
## 2372            68.77401
## 2373            67.51534
## 2376            68.19068
## 2377            67.88946
## 2382            61.34600
## 2387            61.38671
## 2393            61.47270
## 2399            57.18471
## 2408            53.86808
## 2413            54.93225
## 2422            56.04085
## 2424            56.51490
## 2431            79.98573
## 2433            80.34702
## 2434            78.98351
## 2435            79.63864
## 2439            78.14410
## 2443            73.94768
## 2444            73.85914
## 2445            73.80544
## 2457            72.22228
## 2465            65.34800
## 2477            67.33926
## 2482            66.65024
## 2487            57.35935
## 2488            56.50260
## 2491            58.57560
## 2493            56.33145
## 2501            50.89404
## 2502            48.95950
## 2510            80.99026
## 2512            79.86687
## 2514            80.63407
## 2516            79.87535
## 2518            80.62376
## 2521            80.31691
## 2526            81.00702
## 2534            77.86487
## 2536            78.46888
## 2546            68.63360
## 2547            69.25685
## 2551            69.65846
## 2552            69.34732
## 2553            69.53944
## 2555            68.94708
## 2560            68.74060
## 2571            75.79362
## 2573            75.62126
## 2581            68.83205
## 2589            74.45050
## 2604            68.41235
## 2605            69.28158
## 2607            67.90513
## 2611            65.65429
## 2622            58.75733
## 2628            55.25533
## 2629            54.05078
## 2637            73.86940
## 2640            74.18828
## 2643            75.90395
## 2664            65.92786
## 2669            75.21351
## 2675            74.90331
## 2677            74.03319
## 2683            75.94349
## 2686            75.48790
## 2691            70.04140
## 2695            69.86840
## 2697            70.92398
## 2703            67.89668
## 2716            56.62387
## 2720            55.11144
## 2721            55.49390
## 2724            53.47347
## 2729            51.01863
## 2736            70.80682
## 2740            69.07944
## 2741            69.47736
## 2748            76.75885
## 2755            75.18894
## 2761            73.89355
## 2762            73.72997
## 2776            74.28485
## 2779            65.77646
## 2805            76.27514
## 2811            78.24547
## 2813            78.56469
## 2823            76.58712
## 2825            76.80081
## 2831            74.11609
## 2832            71.62497
## 2834            69.45426
## 2836            68.33655
## 2841            69.85779
## 2848            69.18885
## 2850            69.23409
## 2853            64.38059
## 2857            64.54653
## 2863            74.45297
## 2871            71.56684
## 2875            73.38086
## 2877            69.24940
## 2878            73.20412
## 2899            66.70666
## 2902            65.71903
## 2908            58.51361
## 2912            56.73322
## 2913            57.18364
## 2920            51.85048
## 2926            57.16869
## 2931            50.23588
## 2938            48.44372
MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = poly7log.interaction.model_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 3.533711
# RMSE of Poly7Log Model with Categorical variable Status added (not as interaction)
status.poly7logmodel_Preds = predict(status.poly7logmodel, newdata = validate)
as.data.frame(poly2logmodel_Preds)
##      poly2logmodel_Preds
## 1               65.36285
## 6               65.04255
## 7               64.57153
## 9               64.07558
## 10              63.57594
## 24              75.15340
## 28              74.49068
## 33              75.77933
## 35              74.73490
## 36              74.68665
## 42              72.62916
## 43              69.86209
## 48              69.97629
## 49              59.53415
## 57              57.65260
## 59              56.91763
## 60              57.43848
## 79              68.29692
## 80              67.99165
## 82              80.00336
## 105             73.56737
## 108             72.97306
## 115             83.84505
## 124             82.45711
## 129             79.09504
## 130             79.48500
## 136             76.26041
## 137             76.27300
## 151             71.50479
## 156             69.37623
## 157             69.71964
## 159             68.41937
## 164             73.99311
## 168             74.78687
## 174             74.64601
## 176             68.77127
## 182             75.66910
## 184             75.74653
## 186             75.71337
## 190             75.01001
## 193             70.50388
## 194             68.94431
## 201             67.91196
## 204             68.89757
## 206             65.57496
## 209             77.69239
## 210             77.53767
## 213             77.11635
## 218             75.52773
## 221             70.60495
## 223             68.79800
## 226             76.74264
## 232             75.42076
## 240             74.11138
## 242             79.62985
## 247             79.08562
## 258             72.84780
## 259             73.15668
## 264             74.15598
## 278             58.90128
## 285             56.39172
## 287             56.08597
## 288             56.36596
## 289             68.23991
## 296             61.39419
## 297             61.92013
## 298             61.65784
## 306             75.85674
## 307             75.22626
## 312             72.02436
## 318             72.29254
## 338             63.23719
## 339             60.99163
## 345             58.61322
## 351             54.48637
## 356             76.81192
## 368             76.07938
## 371             76.59082
## 375             75.88854
## 386             75.94112
## 402             60.90420
## 406             61.19793
## 409             58.76365
## 415             50.79987
## 418             62.59232
## 419             61.56918
## 426             56.50613
## 429             53.79469
## 430             53.56022
## 446             56.55637
## 448             56.83985
## 450             70.34551
## 451             70.14270
## 452             67.95593
## 453             66.91956
## 459             65.02777
## 460             65.37016
## 465             69.55411
## 468             64.36302
## 478             55.18980
## 480             53.30017
## 482             57.65236
## 492             53.45678
## 493             54.07134
## 503             79.63121
## 505             80.67652
## 509             79.50925
## 511             79.46527
## 513             52.87530
## 516             51.10272
## 518             50.79731
## 523             48.85853
## 527             50.61146
## 532             54.66459
## 537             51.60181
## 545             79.66309
## 555             77.43983
## 556             76.60600
## 559             77.28857
## 577             74.58519
## 580             75.30146
## 596             62.03666
## 601             65.80368
## 603             65.66422
## 614             57.61624
## 626             75.39633
## 627             75.72007
## 635             74.71675
## 642             78.08990
## 645             77.58596
## 646             77.19050
## 655             73.69398
## 658             76.11105
## 665             77.99008
## 673             74.17941
## 686             76.81145
## 698             73.97012
## 699             74.01068
## 701             73.45732
## 720             69.55470
## 729             61.38720
## 732             58.19061
## 751             80.12571
## 752             78.68092
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MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = status.poly7logmodel_Preds)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 3.702815

KNN Model Predictions

library(caret)
fit_cont1 = trainControl(method = "repeatedcv", number = 10, repeats = 1)
set.seed(1364)

knnfit1 = train(Life.expectancy~Adult.Mortality + infant.deaths + Alcohol + percentage.expenditure + Measles + BMI + under.five.deaths + Polio + Total.expenditure + Diphtheria + HIV.AIDS + thinness..1.19.years + thinness.5.9.years + Income.composition.of.resources + Schooling + GDP, data =training, method = "knn", trControl = fit_cont1, tuneGrid = expand.grid(k = c(1:30)))

plot(knnfit1)

updateval = validate[,c("Life.expectancy", "Adult.Mortality", "infant.deaths", "Alcohol", "percentage.expenditure", "Measles", "BMI", "under.five.deaths", "Polio", "Total.expenditure", "Diphtheria", "HIV.AIDS", "thinness..1.19.years","thinness.5.9.years",  "Income.composition.of.resources", "Schooling", "GDP")]

prediction = predict(knnfit1, newdata = updateval)

MSPE = data.frame(Observed = validate$Life.expectancy, 
                  Predicted = prediction)
MSPE$Residual = MSPE$Observed - MSPE$Predicted
MSPE$SquaredResidual = MSPE$Residual^2
sqrt(mean(MSPE$SquaredResidual))
## [1] 5.595665
#cf = confusionMatrix(prediction,updateval$Life.expectancy))
#cf